Question

Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. The shape of the backyard is rectangular, with the length twice as long as the width. What are the dimensions of the backyard? Which quadratic equation would be used to solve for the unknown dimensions?

Answer 1

16 ft by 32ft

Explanation:

Answer 2

The dimensions are
`16` ft by
`32` ft

The quadratic equation is
`W^(2)-256=0`

Explanation:

we know that

the area of rectangle is equal to

`A=W*L`

where

L is the length side of rectangle

W is the width side of rectangle

in this problem

we have

`A=512\ ft^(2)`

so

`512=L*W` -----> equation A

`L=2W` ------> equation B

substitute equation B in equation A

`512=(2W)*W \\ 512=2W^(2) \\2W^(2)-512=0\\W^(2)-256=0`

`W=√(256)=16\ ft`

Find the value of L

`L=2W-----> L=2*16=32\ ft`