# HOW TO TELL IF A TRIANGLE IS A RIGHT TRIANGLE WITH GIVEN SIDES

## About "How to tell if a triangle is a right triangle with given sides"

How to tell if a triangle is a right triangle with given sides :

If a and b are measures of the shorter sides of a triangle, c is the measure of the longest side, and c2 = a2 + b2, then the triangle is a right triangle.

If c2 ≠ a2 + b2, then the triangle is not a right triangle.

let us see some example problems based on the above concept.

Example 1 :

Determine whether the following side measures form right triangles.

20, 21, 29

Solution :

Since the measure of the longest side is 29, let c = 29, a = 20, and b = 21.

Then determine whether c2  =  a2 + b2

c2  =  a2 + b

292 = 202 + 212

841 = 400 + 441

841 = 841

Since c2  =  a2 + b2, the triangle is a right triangle.

Example 2 :

Determine whether the following side measures form right triangles.

8, 10, 12

Solution :

Since the measure of the longest side is 12, let c = 12, a = 10, and b = 8.

Then determine whether c2  =  a2 + b2

c2  =  a2 + b

122 = 102 + 82

144 = 100 + 64

144 ≠ 164

Since c2    a2 + b2, the triangle is not a right triangle.

Example 3 :

Determine whether the following side measures form right triangles.

30, 40, 50

Solution :

Since the measure of the longest side is 50, let c = 50, a = 30, and b = 40.

Then determine whether c2  =  a2 + b2

c2  =  a2 + b

502  =  302 + 402

2500 = 900 + 1600

2500 = 2500

Since c2  =  a2 + b2, the triangle is a right triangle.

Example 4 :

Determine whether the following side measures form right triangles.

6, 12, 18

Solution :

Since the measure of the longest side is 18, let c = 18, a = 6, and b = 12.

Then determine whether c2  =  a2 + b2

c2  =  a2 + b

182  =  62 + 122

324 = 36 + 144

324  180

Since c2    a2 + b2, the triangle is not a right triangle.

Example 5 :

Determine whether the following side measures form right triangles.

24, 30, 36

Solution :

Since the measure of the longest side is 36, let c = 36, a = 24 and b = 30.

Then determine whether c2  =  a2 + b2

c2  =  a2 + b

362 =  242 + 302

1296 = 576 + 900

1296  1476

Since c2    a2 + b2, the triangle is not a right triangle. After having gone through the stuff given above, we hope that the students would have understood "How to tell if a triangle is a right triangle with given sides".

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