Question

if the area of rt angle triangle is 40 and perimetre is 40 find the length of hypotenous

Answer 1

Answer: h = 18 cm

Step-by-step explanation:

Let the hypotenuse AC = h and the other two sides be AB = a and BC = b

By Pythagoras theorem, we have h² = a² + b² → (1)

Given area of ΔABC = 40 sq cm

⇒ ab = 80 → (2)

Given perimeter of ΔABC = 40 cm

That is a + b + h = 40

⇒ a + b = 40 – h

Squaring on both the sides, we get

(a + b)² = (40 – h)²

⇒ a² + b² + 2ab = 1600 – 80h + h²

⇒ h² + 2(80) = 1600 – 80h + h²  From (1) and (2)]

⇒ 160 = 1600 – 80h

⇒ 80h = 1600 – 160 = 1440

∴ h = 18 cm

Thus the length of hypotenuse is 18 cm.