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प्रश्न
The hypotenuse of a right-angled triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.
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उत्तर
Let the length of shortest side = x m
Length of hypotenuse = 2x – 1
and third side = x + 1
Now according to the condition,
(2x – 1)2 = (x)2 + (x + 1)2 ...(By Pythagorus Theorem)
⇒ 4x2 – 4x + 1 = x2 + x2 + 2x + 1
⇒ 4x2 – 4x + 1 = 2x2 - 2x – 1 = 0
⇒ 2x2 – 6x = 0
⇒ x2 – 3x = 0
⇒ x(x – 3) = 0 ...(Dividing by 2)
Either x = 0,
but it is not possible
or
x – 3 = 0,
then x = 3
Shortest side = 3m
Hypotenuse = 2 x 3 – 1 = 6 – 1 – 5
Third side = x + 1 = 3 + 1 = 4
Hence sides are 3, 4, 5 (in m).
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