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

The system of inequalities representing the possible dimensions of the pool, with perimeter greater than 62 meters and width at least 10 meters less than the length, is 2l + 2w > 62 and w ≥ l - 10.

Step-by-step explanation:

The system of inequalities that represents the possible length (l) and width (w) of the pool, given that the perimeter is more than 62 meters and the width is at least 10 meters less than the length, can be set up by defining two inequalities:

The perimeter of a rectangle is defined as P = 2l + 2w. The perimeter is more than 62 meters, so the inequality will be 2l + 2w > 62.

The width is at least 10 meters less than the length, which can be written as w ≥ l - 10.

Therefore, the system of inequalities is:

2l + 2w > 62

w ≥ l - 10

Answer 2

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)`