Question

Which one of these four sets of side lengths will form a right triangle?

Answer 1

To be a right triangle, the hypotenuse^2 must equal side1^2 + side2^2

Only set 2 meets these conditions

8, sq root (29), sq root (35) then squaring these:

64, 29, 35

64 = 29 + 35

Answer 2

Option B is the answer.

Explanation:

We know in a right angle triangle when we apply Pythagoras Theorem, then

(Hypotenuse)² = ( side 1)² + (side 2)²

(A) set (1) ⇒ 6 cm, 7 cm, √12 cm

7² = 6² + (√12)²

49 = 36 + 12 = 48

49 ≠ 48 Therefore, its not the sides of a right triangle.

(B) Set (2) ⇒ 8 in, √29 in, √35 in

8² = (√29)² + (√35)²

64 = 29 + 35

64 = 64 So its a right angle triangle

(C) Set (3) ⇒ √3 mm, 4 mm √5 mm

4² = (√3)² + (√5)²

16 = 3 + 5

16 ≠ 8 Therefore, its not a right angle triangle.

(D) Set (4) ⇒ 9 ft, √26 ft, 6 ft.

9² = (√26)² + 6²

81 = 26 + 36

81 ≠ 62 Therefore, its not a right angle triangle.