Problem: What are the dimensions of the sheet?
A rectangular sheet of metal has an area of 184 square inches and a perimeter of 62 inches.
a = xy = 184 sq in
p = 2x + 2y = 62 in
xy = 184
x = 184/y
2x + 2y = 62
2(184/y) + 2y = 62
368/y + 2y = 62
(368/y + 2y) * y = 62 * y
368 + 2y^2 = 62y
368 + 2y^2 - 62y = 62y - 62y
368 + 2y^2 - 62y = 0
2y^2 - 62y + 368 = 0
(2y^2 - 62y + 368) / 2 = 0 / 2
y^2 - 31y + 184 = 0
We need factors of 184 that give a sum of 31
(y - 23)(y - 8) = 0
y - 23 = 0
y = 23
y - 8 = 0
y = 8
xy = 184
It doesn't matter whether we use 8 or 23 for y, x becomes the other
Either x = 23 and y = 8, or x = 8 and y = 23.
So, the sheet of metal is 23 inches by 8 inches