Question 290059
if the area is 40 square meters, and the perimeter is 26 meters, what is the length and the width? (this was a question on my son's grade 4 math test that is stumping me...)

Wow. 4th grade??? !!!

Let W be the length and L be the length of the rectangle?

Then the area is W*L and the perimeter is 2*W + 2*L. So we have:

1.) W*L = 40
2.) 2*W + 2*L = 26

From 1.) we know that W = 40/L so we can substitute 40/L for W in equation 2.):

2*(40/L) + 2*L = 26

80/L + 2*L = 26

Multiply both sides of this equation by L:

80 + 2L*L = 26*L

80 + 2L^2 = 26*L
2L^2 - 26L + 80 = 0

Divide both sides by 2:

L^2 - 13L + 40 = 0

(L-8)*(L-5) = 40

So L-8 = 0 or L-5 = 0.

L = 8 or L = 5

If L = 8 then W = 40/8 = 5
If L = 5 then W = 40/5 = 8

I don't see an easier way to do this unless it's just to "see" the answer or experiment until you get the right combination for L and W.