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प्रश्न
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
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उत्तर
Let the length of one side of right triangle be = x cm then other side be = (x + 5) cm
And given that hypotenuse = 25 cm
As we know that by Pythagoras theorem,
x2 + (x + 5)2 = (25)2
x2 + x2 + 10x + 25 = 625
2x2 +10x + 25 - 625 = 0
2x2 + 10x - 600 = 0
x2 + 5x - 600 = 0
x2 - 15x + 20x - 600 = 0
x(x - 15) + 20(x - 15) = 0
(x - 15)(x + 20) = 0
So, either
x - 15 = 0
x = 15
Or
x + 20 = 0
x = -20
But the side of right triangle can never be negative
Therefore, when x = 15 then
x + 5 = 15 + 5 = 20
Hence, length of one side of right triangle be 15 cm then other side be 20 cm.
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