math question?

Question

the base of a temple is a rectangle with a perimeter of 300 m. The area of the base is 4400 m squared. what are the dimensions of the base?

Answer 1

we know that P of a rectangle is 2w + 2l. (w = width, l = length)
so 2w + 2l = 300m
and area is l * w
so l * w = 4400
we need to eliminate a variable.
since l * w = 4400, then l = 4400 / w
we can now plug this into l in the first equation to get
2w + 2 (4400/w) = 300
2w + 8800/w = 300
multiply both sides by 2 gives
2w^2 + 8800 = 300w.
subtract 300w to the other side and divide by 2 we get
w^2 -150w + 4400 = 0 which is a quadratic equation.
using the quadratic formula, you get x = 110, or 40.
So the width is either 110 or 40. You can plug either one of these into the beginning equations.
110 * l = 4400
l = 40. (or w = 40 and l = 110)

so it is 40 x 110 meters or 110 meters x 40 meters.

Answer 2

Suppose the base has length L and width W. Then 2L + 2W = 300, and LW = 4400. Solve the first equation for L, substitute into the second equation, and solve the resulting quadratic equation. Then use the first equation to solve for the other dimension.