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?
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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?
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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.
Verified answer
Let the base be pHypotenuse = 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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