Question

The shorter leg of a right triangle is 7 centimeters nbspless than the other leg. Find the length of the two legs if the hypotenuse is 13 centimeter

Answer 1

Answer:

The shorter leg of the right triangle is $5\ cm$

The other leg of the right triangle is $12\ cm$

Step-by-step explanation:

Let

x-----> the shorter leg of a right triangle

y----> the larger leg of a right triangle

we know that

Applying the Pythagoras Theorem

$13^{2}=x^{2} +y^{2}$ ----> equation A

$x=y-7$ ----> equation B

substitute equation B in equation A and solve for y

$13^{2}=(y-7)^{2} +y^{2}\\169=y^{2} -14y+49+y^{2} \\2y^{2}-14y-120=0$

using a graphing tool----> solve the quadratic equation

The solution is $y=12\ cm$

see the attached figure

Find the value of x

$x=12-7=5\ cm$

therefore

The shorter leg of the right triangle is $5\ cm$

The other leg of the right triangle is $12\ cm$