Quadratic Equations

Question

A rectangular garden had dimensions 6m by 8m. Leonard wants to build a path around the garden. He has 120m^2 of bricks. How wide is the pathway?

Answer 1

The area of the rectangular garden is 6*8=48 m^2

Let x be the width of the pathway.

Add 2x to the length and the width of the rectangle.

(6+2x)(8+2x) is the area of both the garden including the pathway.

So subtract 48 from this area.

(6+2x)(8+2x)-48 which is the area of the pathway.

This must be equal to 120m^2

The quadratic equation is

28x+4x^2=120

Factoring out a 4,

x^2+7x-30=0

Applying the quadratic formula, -7+-sqrt. 0f 169/2

x=3 the width of the pathway.

Answer 2

(6 + 2w)(8 + 2w) - 48 = 120

Can you solve for w and answer?