Chapter 9, Problem 15RP

To determine

Tocalculate: The length of side AG.

Answer to Problem 15RP

The length of side AG is 14.5.

Explanation of Solution

Given information:

Side $DC=12,$

Side $CG=7,$

Side $AD=4.$

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

In $\Delta HEG$ ,Draw $\overline{EG}$

Side EG and AG can be calculated by applying Pythagoras Theorems.

In right angled $\Delta EHG$ , we get

  $\begin{array}{l}{\left(EG\right)}^2={\left(HE\right)}^2+{\left(HG\right)}^2\\ {\left(EG\right)}^2=4^2+{12}^2\\ EG=\sqrt{16+144}\\ EG=\sqrt{160}\\ EG=4\sqrt{10}\end{array}$

In right angled $\Delta AEG$ , we get

  $\begin{array}{l}{\left(AG\right)}^2={\left(AE\right)}^2+{\left(EG\right)}^2\\ {\left(AG\right)}^2=7^2+{(}^4\\ {\left(AG\right)}^2=49+160\\ AG=\sqrt{209}\\ AG=14.5\end{array}$