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प्रश्न
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
उत्तर
Let the length of hypotenuse = x cm
then base = (x – 2)cm
and shortest side = x – 4
According to the condition,
(x)2 = (x - 2)2 + (x - 4)2
⇒ x2 = x2 - 4x + 4 + x2 - 8x + 16
⇒ x2 = 2x2 - 12x + 20
⇒ 2x2 - 12x + 20 - x2 = 0
⇒ x2 - 12x + 20 = 0
⇒ x2 - 10x - 2x + 20 = 0
⇒ x(x - 10) -2(x - 10) = 0
⇒ (x - 10)(x - 2) = 0
Either x - 10 = 0,
then x = 10
or
x - 2 = 0,
then x = 2,
but it is not possible as the hypotenuse is the longest side.
∴ Hypotenuse = 10cm
Base = 10 - 2 = 8cm
and shortest side = 10 - 4 = 6cm.
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