Question

the length of a rectangle is 2cm longer than twice its width. find the dimensions of the rectangle if its area is 24cm^2

Answer 1

• 3 cm wide
• 8 cm long

Explanation:

The given relation between length and width can be written as an equation. Let w represent the width. Then the length is 2w+2 and the area is ...

A = LW

A = (2w+2)(w) = 24

w(w+1) = 12 . . . . . . divide by 2

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We know factors of 12 are ...

12 = 1(12) = 2(6) = 3(4)

We see that 4 = 3+1, so ...

w = 3

2w+2 = 8

The dimensions of the rectangle are 3 cm wide by 8 cm long.

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Additional comment

The given quadratic also has negative solution w=-4. Negative values for geometric lengths are extraneous solutions.