Your dad is designing a new garden for your backyard. He has 26 feet of fencing to go around the garden. He wants the length of the garden to be 3 1/2 feet longer than the width. How wide should he make the garden?

4.75 feet

Step-by-step explanation:

Perimeter for any rectangular shape is given by 2(length + width).

Fencing the garden means one wiring the garden along  the perimeter.

Thus, it can be concluded that garden has perimeter of 26 feet as given in question.

Let the width be x feet

given that,  He wants the length of the garden to be 3 1/2 feet longer than the width

thus, length of garden = x + 3 1/2 feet = x + 3.5 feet

if length is x+3.5 feet and width is x feet.

Then perimeter = 2( x+3.5 + x) = 2(2x+3.5) = (4x + 7) feet.

This perimeter will be equal to 26 feet fence

thus,

(4x + 7)  = 26

=> 4x = 26 - 7 = 19

=> x = 19/4 = 4.75 feet

x is width of garden.

Thus, he should make the garden 4.75 feet wide.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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