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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?

Respuesta :

calculista

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

[tex]B=A+24[/tex] -----> equation A

we have that

[tex]B=(x^{2} +11x+24)\ ft^{2}[/tex] -----> equation B

substitute equation B in equation A

[tex]x^{2} +11x+24=A+24[/tex]

Solve for A

[tex]A=x^{2} +11x[/tex]

Factor x

[tex]A=x(x+11)\ ft^{2}[/tex]  ---> 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

[tex]L=(x+11)\ ft[/tex]

[tex]W=x\ ft[/tex]

therefore

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

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