Chapter 4.8, Problem 11P

To determine

To find the length of each legs .

Answer to Problem 11P

The value of leg1 and leg2 is $15m$ and $20m$ .

Explanation of Solution

Given information: Hypotenuse of right triangle is 25m long. The length of one leg is 10m less than twice the other.

Calculation: The length of each legs is obtained as,

Let,

  $a=x$ is leg1, $b=2x-10$ is leg2 and $c=25$ is hypotenuse.

Using the pytagorean theorem $a^2+b^2=c^2$ .

  $\begin{array}{l}{\left(2x-10\right)}^2+x^2={25}^2\\ {\left(2x\right)}^2+100-2\cdot \left(2x\right)\cdot \left(10\right)+x^2=625\\ 4x^2+100-40x+x^2=625\\ 5x^2-40x+100-625=0\\ 5x^2-40x-525=0\\ x^2-8x-105=0\\ x^2+7x-15x-105=0\\ x\left(x+7\right)-15\left(x+7\right)=0\\ \left(x+7\right)\left(x-15\right)=0\\ x=-7,15\end{array}$

Ignore negative value.

  $a=x=15$ is leg1.

  $b=2x-10=2\cdot 15-10=30-10=20$ is leg2.

Hence, the value of leg1 and leg2 is $15m$ and $20m$ .