The area of a rectanglular field is 450 m square and he difference between the lengths of two adjacent angles is 7m. find the length of the shorter side and the perimeter of the rectangle

A = L * W = 450 m^2

L = W+7

So: 450m^2 = (W+7) (W)

450m^2 = W^2 + 7W

W^2 + 7W - 450 = 0

Now to factor the quadratic we need to think of what factors of 450 have a difference of 7?

Well 15*30 = 450, but there difference is 15. So let's try two more ... 25*18 = 450. Is 25-18 = 7?

YES! So we know the factors are:

(W-18) (W+25) = 0

So W-18 = 0, W = 18m

And W+25 = 0, W = - 25m

We can't have a negative length in real life, so the only true solution is W = 18m

Do the shorter side (W) is 18m long

And the longer side (L) = W + 7 = 25

So the perimeter (P) = 2 (L+W) = 2 (25+18)

P = 2 (43) = 86m