Question

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?

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.