Question

Your parents decide to build a rectangular pool in your backyard. They determine that the length of the pool should be 15 feet longer than the width.

Answer 1

The area of the pool is the amount of space it occupies

The expression for the area and the perimeter are $\mathbf{A = 15x + x^2}$ and  $\mathbf{P = 4x +30}$, respectively

Let the dimension of the pool be x and y, where x represents width and y represents length.

So, the relationship between the width and the length is given as:

$\mathbf{y = 15 + x}$

The area of the pool would be:

$\mathbf{A = xy}$

Substitute 15 + x for y

$\mathbf{A = x(15 + x)}$

Open bracket

$\mathbf{A = 15x + x^2}$

And the perimeter of the pool would be

$\mathbf{P = 2(x + y)}$

Substitute 15 + x for y

$\mathbf{P = 2(x +15 + x)}$

$\mathbf{P = 2(2x +15)}$

Open brackets

$\mathbf{P = 4x +30}$

Hence, the expression for the area and the perimeter are $\mathbf{A = 15x + x^2}$ and  $\mathbf{P = 4x +30}$, respectively

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