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The hypotenuse of a right triangle …

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The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of a triangle is 5 cm. Find the lengths of these sides.

Posted by Falguni Akhare 5 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 3 months ago

Let the length of the shorter side b x cm. Then, the length of the longer side = (x + 5) cm.

Since the triangle is right-angled, the sum of the squares of the sides must be equal to the square of the hypotenuse (Pythagoras Theorem).
x² + (x + 5)² = 25²
or x²+ x² + 10x + 25 = 625

or 2x² + 10x - 600 = 0
or x²+ 5x - 300 = 0

or (x + 20) (x - 15) = 0

This gives x = 15 or x = - 20

We reject x = - 20 and take x = 15.
Thus, length of shorter side = 15 cm.
Length of longer side = (15 + 5) cm, i.e., 20 cm.

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