Question

A rectangular sandbox is in the center of a larger rectangular back yard. The sand box

measures (x+6) feet long and 5x feet wide. The yard measures (6x+7) feet long and 8x
feet wide.
What is the area of the yard that is NOT apart of the sandbox?

Answer 1

(43
`x^(2)` - 26x)
`ft^(2)`

Explanation:

Area of the yard that is not pat of the sandbox = Area of the yard - Area of the sandbox

Since both the yard and the sandbox has a rectangular shape, then;

Area of a rectangle = length x width

So that,

Area of the yard = length x width

= (6x+7) x 8x

= (48
`x^(2)` + 56x)
`ft^(2)`

Area of the sandbox = length x width

= (x+6) x 5x

= (5
`x^(2)` + 30x)
`ft^(2)`

Thus,

Area of the yard that is not pat of the sandbox = (48
`x^(2)` + 56x) - (5
`x^(2)` + 30x)

= 48
`x^(2)` + 56x - 5
`x^(2)` - 30x

= (43
`x^(2)` - 26x)
`ft^(2)`

Area of the yard that is not pat of the sandbox is (43
`x^(2)` - 26x)
`ft^(2)`.