Question

A rectangular pool is being created with an area of 578 sq ft. If the width is (2x-3) and the length is twice the width of the pool,

a) What simplified equation could be used to find the area of the pool? (3pts)

Answer 1

The simplified equation that can be used to find the area of the pool is:

`Area=8x^2-24x+18`

To find the area of the rectangular pool, you can use the formula for the area of a rectangle: Area = length × width.

Given that the width of the pool is (2x - 3) and the length is twice the width, the length would be 2 × (2x - 3), which simplifies to 4x - 6.

Area = (4x - 6) × (2x - 3)

Using the distributive property (FOIL method):

Area = (4x × 2x) - (4x × 3) - (6 × 2x) + (6 × 3)

Area = 8x² - 12x - 12x + 18

Combine like terms:

Area = 8x² - 24x + 18

So, the simplified equation for the area of the rectangular pool is:

Area = 8x² - 24x + 18