DETERMINING IF A TRIANGLE IS 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 + b² = 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 + b² = 8² + 10²

= 64 + 100

= 164 ----(2)

From (1) and (2),

c² ≠ 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 + b² = 30² + 40²

= 900 + 1600

= 2500 ----(2)

From (1) and (2),

c² = a² + 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 + b² = 6² + 12²

= 36 + 144

= 180 ----(2)

From (1) and (2),

c² ≠ 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 + b² = 24² + 30²

= 576 + 900

= 1476 ----(2)

From (1) and (2),

c² ≠ a² + b²

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

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