Question

GIVING BRAINLIEST! A rectangular garden has a width of 10 feet and a length of 14 feet. A cement walkway is added around the outside of the garden. The area of the garden and the walkway together are 396 square feet. What is the width of the walkway?
I will give you a hint on how to start:

The new width is 10 + 2x and the new length is 14 + 2x.

Answer 1

Given:

Width of a garden = 10 feet

Length of the garden = 14 feet

Area of the garden and the walkway together = 396 square feet.

To find:

The width of the walkway.

Solution:

A cement walkway is added around the outside of the garden.

Let x be the width of the walkway.

The width of the garden with walkway = 10+2x

The length of the garden with walkway = 14+2x

Area of a rectangle is

$Area=length\times width$

Area of garden and the walkway together is

$Area=(14+2x)\times (10+2x)$

$396=140+28x+20x+4x^2$

$396=140+48x+4x^2$

$396=4(35+12x+x^2)$

Divide both sides by 4.

$99=35+12x+x^2$

$0=35-99+12x+x^2$

$0=-64+12x+x^2$

Splitting the middle term, we get

$x^2+16x-4x-64=0$

$x(x+16)-4(x+16)=0$

$(x+16)(x-4)=0$

Using zero product property, we get

$(x+16)=0\text{ and }(x-4)=0$

$x=-16\text{ and }x=4$

Width of walkway cannot be negative. So, x=4.

Therefore, the width of the walkways is 4 feet.

Answer 2

Answer:

Width = 4 feets

_____________☁️☁️

Hope it helps

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