Knitting: You are knitting a blanket. You want the area of the blanket to be 24ft^2. You want the length of the blanket to be 2 feet longer than the width. What should the dimensions of the blanket be?

Question

Mathematics

Jacey Hartman

9 June, 23:31

Knitting: You are knitting a blanket. You want the area of the blanket to be 24ft^2. You want the length of the blanket to be 2 feet longer than the width. What should the dimensions of the blanket be?

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Answers (1)

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Edward Stone · Answer 1

You can use factors to solve. Determine all the factor pairs of 24, find the two that are two numbers apart.

1, 24 X

2, 12 X

3, 8 X

4, 6 YES!

Algebraic way to solve using Quadratics:

l = 2 + w

A = lw

A = (2 + w) w Substitute (2 + w) for l

24 = (2 + w) w Substitute 24 in for the area

24 = 2w + w^2 Distribute

w^2 + 2w - 24 = 0 Set equal to 0 (put in standard form)

(w + 6) (w - 4) = 0 Factor

w + 6 = 0 and w - 4 = 0 Set each factor equal to 0.

So w = - 6 or w = 4 ... - 6 makes no sense for a length! So the width must be 4 and the length will be 4 + 2, which is 6.