Question

The length of a rectangular garden ABCD is 9 feet more than its width. It is surrounded by a brick walkway 4 feet wide as shown below. Suppose the total area of the walkway is 400 square feet. What are the dimensions of the garden?
PLEASE HELP I KEEP TRYING TO DO IT BUT IT DOESN'T WORK.

Answer 1

Answer:

The dimensions of the garden are

Length $25.5\ ft$  and Width $16.5\ ft$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y ---> the width of the rectangular garden

Aw ----> the area of the walkway

we know that

$x=y+9$ ----> equation A

$Aw=(x+8)(y+8)-xy$

$Aw=400\ ft^{2}$

so

$400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy$

$400=8x+8y+64$ ----> equation B

Substitute equation A in equation B

$400=8(y+9)+8y+64$

$400=8y+72+8y+64$

$400=16y+136$

$16y=400-136$

$y=16.5\ ft$

Find the value of x

$x=16.5+9=25.5\ ft$

therefore

The dimensions of the garden are

Length $25.5\ ft$

Width $16.5\ ft$