What are the possible values for the third side of a triangle whose two sides are 12cm and 5cm?

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Isosceles triangle calculator is the best choice if you are looking for a quick solution to your geometry problems. Find out the isosceles triangle area, its perimeter, inradius, circumradius, heights and angles - all in one place. If you want to build a kennel, find out the area of Greek temple isosceles pediment or simply do your maths homework, this tool is here for you. Experiment with the calculator or keep reading to find out more about the isosceles triangle formulas.

An isosceles triangle is a triangle with two sides of equal length, which are called legs. The third side of the triangle is called base. Vertex angle is the angle between the legs and the angles with the base as one of their sides are called the base angles.

Here are the most important properties of isosceles triangles:

• It has an axis of symmetry along its vertex height;
• Two angles opposite the legs are equal in length; and
• The isosceles triangle can be acute, right, or obtuse, but it depends only on the vertex angle (base angles are always acute)

The equilateral triangle is a special case of an isosceles triangle. You can learn about all the possible types of triangles in the classifying triangles calculator.

To calculate the isosceles triangle area, you can use many different formulas. The most popular ones are the equations:

1. Given leg a and base b:

   area = (1/4) × b × √( 4 × a² - b² )

2. Given h height from apex and base b or h2 height from other two vertices and leg a:

   area = 0.5 × h × b = 0.5 × h2 × a

3. Given any angle and leg or base

   area = (1/2) × a × b × sin(base_angle) = (1/2) × a² × sin(vertex_angle)

Also, you can check our triangle area calculator to find out other equations, which work for every type of triangle, not only for the isosceles one.

To calculate the isosceles triangle perimeter, simply add all the triangle sides:
perimeter = a + a + b = 2 × a + b

Isosceles triangle theorem, also known as the base angles theorem, claims that if two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Also, the converse theorem exists, stating that if two angles of a triangle are congruent, then the sides opposite those angles are congruent.

A golden triangle, which is also called sublime triangle is an isosceles triangle in which the leg is in the golden ratio to the base:

a / b = φ ~ 1.618

The golden triangle has some unusual properties:

• It's the only triangle with three angles in 2:2:1 proportions
• It's the shape of the triangles found in the points of pentagrams
• It's used to form a logarithmic spiral

Let's find out how to use this tool on a simple example. Have a look at this step-by-step solution:

1. Determine what is your first given value. Assume we want to check the properties of the golden triangle. Type 1.681 inches into leg box.
2. Enter second known parameter. For example, take a base equal to 1 in.
3. All the other parameters are calculated in the blink of an eye! We checked for instance that isosceles triangle perimeter is 4.236 in and that the angles in the golden triangle are equal to 72° and 36° - the ratio is equal to 2:2:1, indeed.

You can use this calculator to determine different parameters than in the example, but remember that there are in general two distinct isosceles triangles with given area and other parameter, e.g. leg length. Our calculator will show one possible solution.

To compute the area of an isosceles triangle with leg a and base b, follow these steps:

1. Apply the Pythagorean theorem to find the height: √( a² - b²/4 ).

2. Apply the standard triangle area formula, i.e., multiply base b by the height found in Step 1 and then divide by 2.

3. That is, the final formula we got is:

   area = ½ × b × √( a² - b²/4 )

We compute the perimeter of an isosceles triangle with leg a and base b with the help of the formula perimeter = 2 × a + b. This formula makes use of the fact that the two legs of an isosceles triangle are of equal length.

The answer is 6.93. To derive it, we can use the formula area = ½ × b × √( a² - b²/4 ) with a = b = 4.

Alternatively, we can notice that, in fact, we have here an equilateral triangle: the are formula simplifies to area = a² × √3 / 4 with a = 4.

Question 23 Exercise 10.1

Next

Answer:

Solution:

Let the length of the third side be x cm.

The length of the other two sides is 12 cm and 14 cm.

Now, the Perimeter of triangle = 36 cm

12+14+x=36

26+x=36

x=36-26=10

Thus, the length of third side is 10 cm.

Video transcript

Hello students, welcome to the Lido learning. So here the question is two supplementary angles are Phi x minus 82 degrees + 4 x + 73 degrees. So here we have to find the value of the X. So let us write it starts the answer. So here solution is supplementary angles are 180 degrees, right? So here the equation is 5X minus 82 degrees plus 44 x + 73 degrees is 180 degrees. So you're freaking observe 9x minus 9 9 x minus 9 is equal to 180 degrees. So 9 x if we sent to the right-hand side we get 9x is equals to 1 89. So here if we send mine from multiplying to the right-hand side dividing. Sorry. Sorry. Sorry dividing X equals to one eighty-nine by nine is equal to the answer the final answer we get the x value is 21 degrees. Thank you for watching our video. A subscriber to our Channel and feel free to ask doubts in the comment section below. Thank you.

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Triangle is a closed figure which is formed by three line segments. It consists of three angles and three vertices. The angles of triangles can be the same or different depending on the type of triangle. There are different types of triangles based on line and angles properties.

Properties of a Triangle:

1. Each triangle has 3 sides and 3 angles.

2. Sum of all the angles of triangles is 180°

3. Perimeter of a triangle is the sum of all three sides of the triangle.

4. A triangle has 3 vertices.

Types of Triangles based on line Properties

Scalene Triangle: Scalene Triangle is a type of triangle in which all the sides are of different lengths. All the angles of a scalene triangle are different from one another.

Isosceles Triangle: Isosceles Triangle is another type of triangle in which two sides are equal and the third side is unequal. In this triangle, the two angles are also equal and the third angle is different.

Right-angled Triangle: A right-angled triangle is one that follows the Pythagoras Theorem and one angle of such triangles is 90 degrees which is formed by the base and perpendicular. The hypotenuse is the longest side in such triangles.

Equilateral Triangle: An equilateral triangle is a triangle in which all the three sides are of equal size and all the angles of such triangles are also equal.

Finding Third Side of a Triangle given Two Sides

Lets assume that the triangle is Right Angled Triangle because to find a third side provided two sides are given is only possible in a right angled triangle.

We know that the right-angled triangle follows Pythagoras Theorem

According to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side. 

(Perpendicular)2 + (Base)2 = (Hypotenuse)2 

Using the above equation third side can be calculated if two sides are known.

Example: Suppose two sides are given one of 3 cm and the other of 4 cm then find the third side.

Lets take perpendicular P = 3 cm and Base B = 4 cm.

using Pythagoras theorem 

P2 + B2 = H2

(3)2 + (4)2 = H2

9 + 16 = H2

25 = H2

H = 5

Sample Questions

Question 1: Find the measure of base if perpendicular and hypotenuse is given, perpendicular = 12 cm and hypotenuse = 13 cm.

Solution: 

Perpendicular = 12 cm

Hypotenuse = 13 cm

Using Pythagoras Theorem 

P2 + B2 = H2

B2 = H2 – P2

B2 = 132 – 122

B2 = 169 – 144

B2 = 25

B = 5

Question 2: Perimeter of the equilateral triangle is 63 cm find the side of the triangle.

Solution: 

Perimeter of an equilateral triangle =  3×side

3×side = 64

side = 63/3

side = 21 cm

Question 3: Find the measure of the third side of a right-angled triangle if the two sides are 6 cm and 8 cm.

Solution: 

Perpendicular = 6 cm

Base = 8 cm

Using Pythagoras Theorem

H2 = P2 + B2 

H2 = P2 + B2

H2 = 62 + 82 

H2 = 36 + 64

H2 = 100

H = 10 cm

Question 4: Find whether the given triangle is a right-angled triangle or not, sides are 48, 55, 73?

Solution: 

A right-angled triangle follows the Pythagorean theorem so we need to check it .

Sum of squares of two small sides should be equal to the square of the longest side

so 482 + 552 must be equal to 732

2304 + 3025 = 5329 which is equal to 732 = 5329

Hence the given triangle is a right-angled triangle because it is satisfying the Pythagorean theorem.

Question 5: Find the hypotenuse of a right angled triangle whose base is 8 cm and whose height is 15 cm?

Solution: 

Using Pythagorean theorem, a2 + b2 = c2

So 82 + 152 = c2  

hence c = √(64 + 225)

          c = √289

          c = 17 cm

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