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General

General

Easy

Question

A rectangle has a width that is twice the length. If the area of the rectangle is represented by the expression 18x² + 48x + 32, what expression represents the length of the rectangle?

hint Hint:

Using the formula area = length × breadth . find the sides of the rectangle by factoring the area.

The correct answer is: 3x + 4 and 6x + 8 are the length and width of the rectangle respectively.

Ans:- 3x + 4 and 6x + 8 are the length and width of the rectangle respectively.
Let the length of rectangle be l
Rectangle has a width that is twice the length
Then width = 2l
Area = length × width = $2 l squared$
Given area = $18 x squared plus 48 x plus 32$
Taking away common factor 2 we get , $2 open square brackets 9 x squared plus 24 x plus 16 close square brackets$
Now write $9 x squared text as end text left parenthesis 3 x right parenthesis squared comma 24 x text as end text 2 left parenthesis 3 x right parenthesis left parenthesis 4 right parenthesis text and end text 16 text as end text 4 squared$
Area = $2 open square brackets left parenthesis 3 x right parenthesis squared plus 2 left parenthesis 3 x right parenthesis left parenthesis 4 right parenthesis plus 4 squared close square brackets equals 2 left parenthesis 3 x plus 4 right parenthesis squared$
$2 l squared equals 2 left parenthesis 3 x plus 4 right parenthesis squared not stretchy rightwards double arrow l equals 3 x plus 4$
Length = l = 3x + 4
Width = 2l = 2(3x + 4) = 6x + 8

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