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The hypotenuse of a right triangle is 13 cm. If one leg is 7 cm longer than the other, which equation gives the shorter leg $x$ ?

Class 10Quadratic Word ProblemsAlgebra — Quadratics

A $x^{2} + (x + 7)^{2} = 1 3^{2}$
B $x^{2} + (x + 7)^{2} = 13$
C $x + (x + 7) = 13$
D $x (x + 7) = 169$

Step-by-Step Solution

By Pythagoras, sum of squares of legs equals square of hypotenuse:

x^{2} + (x + 7)^{2} = 1 3^{2}

.

Answer: A)

x^{2} + (x + 7)^{2} = 1 3^{2}

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