# The perimeter of a rectangle is 80 x. The base is 7 times the height. In terms of x, what are the...

## Question:

The perimeter of a rectangle is {eq}80 x {/eq}. The base is 7 times the height. In terms of {eq}x {/eq}, what are the dimensions of the rectangle. What is the area?

## Perimeter and Area of a Rectangle

A quadrilateral in which opposite sides are parallel and equal to each other is called a rectangle.

A rectangle has all four angles of {eq}90^{\circ}. {/eq}

There are two diagonals in a rectangle.

#### Perimeter of a rectangle

{eq}\displaystyle P = 2 \times (B + H) {/eq}

here {eq}P = {/eq} perimeter

{eq}B = {/eq} length of the base of the rectangle

{eq}H = {/eq} height of the rectangle

#### Area of the Rectangle

{eq}A = B \times H {/eq}

{eq}A = {/eq} area of the rectangle in square units

Given that the perimeter of the rectangle is 80x and the base is 7 times the height off the rectangle-

{eq}\displaystyle B = 7 \times H ----------(1) {/eq}

{eq}\displaystyle P = 80x {/eq}

{eq}\displaystyle 2(B+H) = 80x {/eq}

{eq}\displaystyle B+H = 40x {/eq}

from equation(1) put the value of Base-

{eq}\displaystyle 7 \times H + H = 40x {/eq}

{eq}\displaystyle 8H = 40x {/eq}

{eq}\displaystyle H = \frac{40x}{8} = 5x {/eq}

from the equation(1)-

{eq}\displaystyle B = 7 \times (5x) {/eq}

{eq}\displaystyle B = 35x {/eq}

So the base and height of the given rectangle are 35x and 5x respectively.

Now the area of the rectangle-

{eq}\displaystyle A = B \times H {/eq}

{eq}\displaystyle A = (35x)(5x) {/eq}

{eq}\displaystyle A = 175x^{2} {/eq} square units