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प्रश्न
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
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उत्तर
Let the shortest side = x
Hypotenuse = 2x + 1
and third side = x + 7
According to the condition,
(2x + 1)2 = x2 + (x + 7)2
⇒ 4x2 + 4x + 1 = x2 + x2 + 14x + 49
⇒ 4x2 + 4x + 1 - 2x2 - 14x - 49 = 0
⇒ 2x2 - 10x - 48 = 0
⇒ x2 - 5x - 24 = 0 ...(Dividing by 2)
⇒ x2 - 8x + 3x - 24 = 0
⇒ x(x - 8) + 3(x - 8) = 0
⇒ (x - 8)(x + 3) = 0
EIther x - 8 = 0,
then x = 8
or
x + 3 = 0,
then x = -3,
but it is not possible as it is negative.
∴ Shortest side = 8m
Third side
= x + 7
= 8 + 7
= 15m
and hypotenuse
= 2x + 1
= 8 x 2 + 1
= 16 + 1
= 17m.
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