Question

A park consists of a patch of grass with a brick path around the perimeter. The patch of grass is 18 ft wide and 15 ft tall. The area of the entire park including both grass and path is 360 sq feet. Write a quadratic equation that could be used to determine the width of the brick path, x
I really need help asap

Answer 1

Answer:

$A_{t} = 270\,ft^{2} + (66\,ft)\cdot x + 4\cdot x^{2}$

Step-by-step explanation:

The total area is the sum of the areas from the patch of grass and the brick path:

$A_{t} = A_{g} + A_{p}$

$A_{t} = (18\,ft)\cdot (15\,ft) + 2\cdot x \cdot (18\,ft) + 2\cdot x \cdot (15\,ft) + 4\cdot x^{2}$

$A_{t} = 270\,ft^{2} + (66\,ft)\cdot x + 4\cdot x^{2}$