SOLUTION: A square and a rectangle have the same area. The square's length is x and width is x for the rectangle's length is 2x-3 and width is x-2. What is the numerical value of the rectang

Algebra ->  Human-and-algebraic-language -> SOLUTION: A square and a rectangle have the same area. The square's length is x and width is x for the rectangle's length is 2x-3 and width is x-2. What is the numerical value of the rectang      Log On


   

Question 647749: A square and a rectangle have the same area. The square's length is x and width is x for the rectangle's length is 2x-3 and width is x-2. What is the numerical value of the rectangle's perimeter?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A square and a rectangle have the same area.
The square's length is x and width is x
for the rectangle's length is 2x-3 and width is x-2.
What is the numerical value of the rectangle's perimeter?
:
"A square and a rectangle have the same area."
(2x-3)(x-2) = x^2
2x^2 - 4x - 3x + 6 = x^2
2x^2 - x^2 - 7x + 6 = 0
x^2 - 7x + 6 = 0
Factors to
(x-1)(x-6) = 0
x = 6 is the only reasonable solution
then
2(6)-3 = 9 is the length of the rectangle
and
6 - 2 = 4 is the width
Find the perimeter
2(9) + 2(4) = 26
:
:
Check this by finding the areas
6^2 = 36
9*4 = 36