# DETERMINING IF A TRIANGLE IS A RIGHT TRIANGLE

Let a, b and c be the sides of a triangle and c be the longest side.

If a, b and c are the sides of a right triangle, then by Pythagorean theorem,

c2 = a2 + b2

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

In each case, determine if the side lengths lengths form a right triangle.

Example 1 :

20, 21, 29

Solution :

Let a = 20, b = 21 and c = 29.

c2 = 292

= 841 ----(1)

a2 + b= 202 + 212

= 400 + 441

= 841 ----(2)

From (1) and (2),

c2 a2 + b2

The side lengths 20, 21 and 29 form a right triangle.

Example 2 :

8, 10, 12

Solution :

Let a = 8, b = 10 and c = 12.

c2 = 122

= 144 ----(1)

a2 + b= 82 + 102

= 64 + 100

= 164 ----(2)

From (1) and (2),

c≠ a2 + b2

The side lengths 8, 10 and 12 do not form a right triangle.

Example 3 :

30, 40, 50

Solution :

Let a = 30, b = 40 and c = 50.

c2 = 502

= 2500 ----(1)

a2 + b= 302 + 402

= 900 + 1600

= 2500 ----(2)

From (1) and (2),

ca2 + b2

The side lengths 30, 40 and 50 form a right triangle.

Example 4 :

6, 12, 18

Solution :

Let a = 6, b = 12 and c = 18.

c2 = 182

= 324 ----(1)

a2 + b= 62 + 122

= 36 + 144

= 180 ----(2)

From (1) and (2),

c≠ a2 + b2

The side lengths 6, 12 and 18 do not form a right triangle.

Example 5 :

24, 30, 36

Solution :

Let a = 24, b = 30 and c = 36.

c2 = 362

= 1296 ----(1)

a2 + b= 242 + 302

= 576 + 900

= 1476 ----(2)

From (1) and (2),

c≠ a2 + b2

The side lengths 24, 30 and 36 do not form a right triangle.

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