Chapter 8, Problem 17CT

To determine

To find: the value of x

Answer to Problem 17CT

The value of x is $24$ .

Explanation of Solution

Given Information: A right triangle with measure of altitude being 7 units

Formula used:

The relationship between the legs of right triangle (shown in figure below) a , b and its hypotenuse c is obtained by using Pythagoras theorem.

  

It can be expressed as,

  $\begin{array}{l}{c}^2=a^2+b^2\\ c=\sqrt{a^2+b^2}\end{array}$

Calculation: Consider the figure given below.

  

The value of x can be calculated by using the Pythagoras theorem as,

  $\begin{array}{c}{\left(x+1\right)}^2=x^2+7^2\\ x^2+2x+1=x^2+7^2\\ 2x=49-1\\ x=24\end{array}$