Problema Solution
The length of a rectangular garden is nineteen feet less than the perimeter. The area of the rectangle is two thousand, five hundred thirty-seven square feet. What are the dimensions of the rectangle?
Answer provided by our tutors
let
l = the length of the rectangular garden, l>0
w = the width of the rectangular garden, w>0
P = 2(l + w) is the perimeter of the rectangular garden
A = l*w is the area of the rectangular garden
The length of a rectangular garden is nineteen feet less than the perimeter
l = 2(l + w) - 19
l = 19 - 2w
The area of the rectangle is two thousand, five hundred thirty-seven square feet
l*w = 2537
plug l = 19 - 2w into the last equation
(19 - 2w)w = 2537
l = 2(l + 2537/l) - 19
by solving we find that the roots are complex numbers
click here to see the step by step solution of the equation
thus there is no such rectangle. the problem has no solution.