Question

the perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?

Answer 1

Let

W--------> the width of a rectangular pool

L--------> the length of a rectangular pool

P-------> Perimeter of the rectangular pool

we know that

Perimeter of the rectangular pool is equal to

$P=2W+2L$

$2W+2L \geq 62$

simplify

$W+L \geq 31$ -------> inequality $1$

$W \geq (L-10)$ -------> inequality $2$

using a graph tool

see the attached figure

the solution of the system is the shaded area (Negative lengths are not being considered in the shaded area)

therefore

the answer is

The system of inequalities that represents the possible lengths and the possible widths of the pool is

$W+L \geq 31$

$W \geq (L-10)$