Question

You are making a walkway around part of a swimming pool. The dimensions of the swimming pool are 18 and 25, while the dimensions of the walkway are x. Write a polynomial that expresses the area of the swimming pool.

Answer 1

Answer:

$A = 4x^2 + 86x + 450$

Step-by-step explanation:

Given

$Walkway = x$

$Length = 18$

$Width = 25$

Required:

The area of the swimming pool

Assume the walkway will be on the 4 sides of the swimming pool.

The total length (L) of the swimming pool will be:

$L = 18 + x + x$

$L = 18 + 2x$

The total width (W) will be:

$W = 25 + x + x$

$W = 25 + 2x$

The area (A) is:

$A = L * W$

$A = (18 + 2x) * (25 + 2x)$

Expand bracket

$A = 18 * 25 + 18 * 2x + 25 * 2x + 2x * 2x$

$A = 450 + 36x + 50x + 4x^2$

$A = 450 + 86x + 4x^2$

Reorder

$A = 4x^2 + 86x + 450$