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alisha [4.7K]
3 years ago
7

The width,w, of a rectangular garden is X -2 the area of the garden is X^3-2X-4 what is an expression for the length of the gard

en?
A. X^2-2x-2
B. X^2+2x-2
C. X^2-2x+2
D. X^2+2x+2

Mathematics
2 answers:
Lunna [17]3 years ago
6 0

Answer:

D. x^2+2x+2

Step-by-step explanation:

We know that,

The area of a rectangle is,

A = l × b,

Where, l is the length of the rectangle,

w is the width of the rectangle,

Given,

A = x^3-2x-4

w=(x-2)

By substituting values,

x^3-2x-4=(x-2)l

\implies l = \frac{x^3-2x-4}{x-2}=x^2+2x+2 ( By long division shown below )

Hence, the length of the rectangular garden is x^2+2x+2

Option D is correct.

slamgirl [31]3 years ago
3 0
A=lw \Rightarrow l=\frac{A}{w}
A - area, l - length, w - width

w=x-2 \\
A=x^3-2x-4 \\ \\
l=\frac{x^3-2x-4}{x-2}=\frac{x^3-2x^2+2x^2-4x+2x-4}{x-2}=\frac{x^2(x-2)+2x(x-2)+2(x-2)}{x-2}= \\
=\frac{(x^2+2x+2)(x-2)}{x-2}=x^2+2x+2

The answer is D. x²+2x+2.
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