# Geometry If the hypothenuse of right triangle of 26 cm long and one cathetus 14 cm longer than the other , find the lengths of the legs of triangle. It is given that the hypotenuse of a right triangle is 26 cm long and one leg is 14 cm longer than the other.

Let the length of the shorter leg be x , the other leg is x + 14

AS it is a right triangle use hypotenuse theorem...

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It is given that the hypotenuse of a right triangle is 26 cm long and one leg is 14 cm longer than the other.

Let the length of the shorter leg be x , the other leg is x + 14

AS it is a right triangle use hypotenuse theorem to write

x^2 + (x + 14)^2 = 26^2

=> x^2 + x^2 + 14^2 + 28x = 26^2

=> 2x^2 + 28x + 14^2 - 26^2 = 0

=> x^2 + 14x -240 = 0

=> x^2 + 24x - 10x - 240 = 0

=> x(x + 24) - 10(x + 24) = 0

=> (x - 10)(x + 24) = 0

We only take x = 10 as length cannot be negative

The lengths of the legs of the triangle are 10 and 24.

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