Question 1028253
perimeter = 204
area = 2565


if x = length and y equal width, then the following formulas apply.


2x + 2y = 204
x * y = 2565


in the second formula of x * y = 2565, solve for y to get y = 2565 / x


in the first formula of 2x + 2y = 204, replace y with 2565 / x to get:


2x + 2 * (2565 / x) = 204x


multiply both sides of this equation by x to get:


2x^2 + 2 * 2565 = 204x


simplify to get 2x^2 + 5130 = 204x


subtract 204x from both sides of this equation to get:


2x^2 - 204x + 5130 = 0


this is a quadratic equation that can be solved by factoring or using the quadratic formula, or by graphing.


i solved using the quadratic formula and got x = 45 or x = 57.


if x * y = 2565, then:


if x = 45, y = 57


if x = 57, y = 45


you have the length is equal to 45 and the width is equal to 57, or you have the length is equal to 57 and the width is equal to 45.


perimeter = 2 * length + 2 * width = 2 * (length + width) = 2 * (45 + 57) = 2 * 102 = 204.


you have area = length * width = 45 * 57 = 2565.


numbers look good.


that's your answer.