Question

The hypotenuse of a right triangle is 6 m more than twice the shortest side. If the third side is 2 m less than the hypotenuse, find the hypotenuse of the triangle. 

(a) 24 m 

(b) 34 m 

(c) 26 m 

(d) 10 m

Answer 1

(c) 26 m

Let the shortest side of the triangle be x m. 

Then, hypotenuse = (2x + 6) m 

Third side = (2x + 6) – 2 = (2x + 4) m 

By Pythagoras’ Theorem, 

(2x + 6)² = (2x + 4)² + x² 

⇒ 4x² + 24x + 36 = 4x² + 16x + 16 + x² 

⇒ x² – 8x – 20 = 0 

⇒ x² – 10x + 2x – 20 = 0

⇒ (x – 10) (x + 2) = 0 

⇒ x = 10 or –2 

∴ x cannot be negative, x =10 

∴ Hypotenuse = (2 ×10 + 6) m = 26 m