The hypotenuse of a right angled triangle is $25$ cm. The other two sides are such that one is $5$ cm longer than the other. Their lengths (in cm) are:

10, 15

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20, 25

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15, 20

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25, 30

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Solution

The correct option is B $15, 20$
Given: Hypotenuse of right triangle $= 25$ cm
Let the other sides be $x$ and $x + 5$
Thus, By Pythagoras Theorem:
$25^{2} = x^{2} + (x + 5)^{2}$
$625 = x^{2} + x^{2} + 25 + 10 x$
$2 x^{2} + 10 x - 600 = 0$
$x^{2} + 5 x - 300 = 0$
$x^{2} + 20 x - 15 x - 300 = 0$
$(x + 20) (x - 15) = 0$
$x = 15, - 20$
Thus, the other two sides are $15$ cm and $20$ cm.

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