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

Answer:

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

Step-by-step 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