Chapter 8.CR, Problem 1CR

To determine

To find:

The area and perimeter of given figure.

Answer to Problem 1CR

Solution:

The area is $\left(x^2-2x\right){\text{ft}}^{\text{2}}$ and perimeter is $\left(4x-4\right)\text{ft}$.

Explanation of Solution

Given:

The given figure is,

Formula used:

The area of rectangle is,

$A=l\times b$

Here, $l$ is the length of the rectangle and $b$ is the breadth of rectangle.

The perimeter of rectangle is,

$P=2\left(l+b\right)$

Calculation:

Consider the given figure.

Figure (1)

Here, length of rectangle $\left(l\right)$ is $x\text{ft}$ and breadth $\left(b\right)$ is $\left(x-2\right)\text{ft}$.

Substitute $x$ for $l$ and $\left(x-2\right)$ for $b$ in formula of area of rectangle.

$\begin{array}{rll}A& =& x\times \left(x-2\right)\\ & =& x^2-2x\end{array}$

Substitute $x$ for $l$ and $\left(x-2\right)$ for $b$ in formula of perimeter of rectangle.

$\begin{array}{rll}P& =& 2\left(x+x-2\right)\\ & =& 2\left(2x-2\right)\\ & =& 4x-4\end{array}$

Hence, the area is $\left(x^2-2x\right){\text{ft}}^{\text{2}}$ and perimeter is $\left(4x-4\right)\text{ft}$.