Question

The hypotenuse if right angled triangle is 6. cm more than twice of the smallest side. length of the third side is 2.cm less than it's hypotenuse. find lengths of its sides​

Answer 1

Answer:

Step-by-step explanation:

Solution :-

Let the shortest side of the triangle be x cm.

its hypotenuse = (2x + 6) cm.

Its third side = (2x + 6 - 2) cm = (2x + 4) cm

According to the Question,

By using Pythagoras's theorem, we have

⇒ (2x + 6)² = x² + (2x + 4)²

⇒ 4x² + 24x + 36 = 5x² + 16x + 16

⇒ x² - 8x - 20 = 0

⇒ x² - 10x + 2x - 20 = 0

⇒ x(x - 10) + 2(x - 10) = 0

⇒ (x - 10) (x + 2) = 0

⇒ x - 10 = 0 or x + 2 = 0

⇒ x = 10, - 2 (As x can't be negative)

⇒ x = 10

Shorter side = x = 10 cm

longer side = 2 × 10 + 4 = 24 cm

Hypotenuse = 2 × 10 + 6 = 26 cm.

Hence, the sides are 10 cm, 24 cm and 26 cm.