Question

The hypotenuse of a right angled triangle is 6 cm more than twice the shortest side. If the third

side is 2 cm less than the hypotenuse, what are the sides of the triangle in cm?

Answer 1

Let the base be p
Hypotenuse = 2p +6
Perpendicular = 2p + 4


By Pythagoras theoram

(2p+6)^2 = (2p+4)^2 +p^2
=> 4p^2 +36 + 24p = 4p^2 + 16 +16p +p^2
=> 36+ 24p = p^2 + 16p + 16
=> p^2 - 8p - 20 = 0
=> p^2 - 10p +2p - 20 = 0
=> p(p-10) +2(p-10) = 0
=> (p-10)(p+2) = 0

p = 10 and - 2
Length can't be negative
So,
p = 10
Base = 10
Perpendicular = 24
Hypotenuse = 26


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Answer 2

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 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.