Question

Seth has a garden with dimensions 9 feet long times 8 feet wide he wants to enlarge the garden to an area of 120 ft.² how much farther will he need to extend the length of the garden to attain his desired area

Answer 1

Answer:

6 ft longer (total length of 15ft)

Step-by-step explanation:

the initial dimensions are:

length: $l=9ft$

width: $w=8ft$

the area area of the garden is given by:

$a=l*w$

so the original area is:

$a=9ft*8ft=72ft^2$

Since we need the area to be $120ft^2$, and we can only change the length, the width will still be 8ft.

We substitute the value of the new area and the width to the equation for the area:

$a=l*w\\120ft^2=l*8ft$

and we clear for the new length:

$l=\frac{120ft^2}{8ft}\\ \\l=15$

The length of the garden for the area to be $120ft^2$, must be 15ft.

This means that if originally the length was 9 ft, now it has to be 6 ft longer.