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Q9.

Expert-verified
Found in: Page 292

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# Find the value of $x$ from the given figure.

The value of $x$ is $25$.

See the step by step solution

## Step 1. Given information.

The given figure is observed that a rectangle.

## Step 2. Theorem used.

We use Pythagoras Theorem.

Pythagoras Theorem state that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

## Step 3. Now find the value.

The opposite sides of the rectangle are equal.

$\begin{array}{l}AB=24\\ DC=24\end{array}$

Calculation:

In $\Delta ADC$

We use Pythagoras Theorem.

$\begin{array}{l}{x}^{2}={7}^{2}+{24}^{2}\\ {x}^{2}=49+576\\ {x}^{2}=625\end{array}$

Taking square root we get.

$x=±\sqrt{625}$

$x=±25$

Since, distance is a positive quantity. So, we neglect negative sign.

Therefore, the value of $x$ is $25$.