Question

A rectangular flower bed is enlarged so that its area increases by 24 ft². The enlarged flower bed is a rectangle and its area is x2+11x+24 ft².

Which expressions represent the dimensions of the flower bed before the increase?

Answer 1

The dimensions of the flower bed before the increase are x ft by (x+11) ft

Explanation:

Let

A -----> the area of the flower bed before the increase

B -----> the area of the enlarged flower bed

we know that

`B=A+24` -----> equation A

we have that

`B=(x^(2) +11x+24)\ ft^(2)` -----> equation B

substitute equation B in equation A

`x^(2) +11x+24=A+24`

Solve for A

`A=x^(2) +11x`

Factor x

`A=x(x+11)\ ft^(2)` ---> area of the flower bed before the increase

Remember that the area of a rectangle is equal to multiply the length by the width

so

`L=(x+11)\ ft`

`W=x\ ft`

therefore

The dimensions of the flower bed before the increase are x ft by (x+11) ft