Question

The length of a swimming pool is 8 m longer than it's width and the area is 105m²​

Answer 1

Below

Explanation:

The area of the swimming pool is

● A = L × w where L is the length and w is the width

The length is 8 m more than the width L = w + 8

● A = (w+8)×w

● A = w^2 +8w

● 105 = w^2 + 8w

● w^2 + 8w - 105 = 0

This is a quadratic equation.

We will solve by graphing it using a graphing tool

The solutions are the intersection points with the x-axis

We will only take the positive solution since the width can't be negative.

The solution is 7 (picture below)

● w = 7 m

The length is

● L = w + 8

● L = 7 + 8

● L = 15 m

Answer 2

width= 7m

Explanation:

Area= L×W

L= (x+8)m

W=8m

105m²= (x+8)m × (x)m

105m²= x² + 8x

-x² - 8x + 105= 0

(x-7) (x+15) = 0

x= 7 x= -15

x=width = 7m