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pashok25 [27]
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
1 answer:
Elan Coil [88]3 years ago
6 0
A=wl \Rightarrow 
l=\frac{A}{w}
l - length, A - area, w - width

A=x^3-2x-4 \\
w=x-2 \\ \\
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.
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Step 2: substitute s from the formula for the perimeter into the formula for the area.

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