SOLUTION: The perimeter of a rectangle is 20 meters. If the length is increased by four times the width, the sum is 19 meters. What are the dimensions of the rectangle? What is its area?
Question 168630: The perimeter of a rectangle is 20 meters. If the length is increased by four times the width, the sum is 19 meters. What are the dimensions of the rectangle? What is its area? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is 20 meters. If the length is increased by four
times the width, the sum is 19 meters. What are the dimensions of the rectangle?
What is its area?
:
Original equation
2L + 2W = 20
Simplify divide by 2
L + W = 10; the sum of the length and width of the original rectangle
or
L = (10-W); we can use for substitution
:
"If the length is increased by four times the width, the sum is 19 meters."
(L+4W) + W = 19
L + 5W = 19
:
Substitute (10-W) for L
10 - W + 5W = 19
4W = 19 - 10
4W = 9
W =
W = 2.25; width of the original rectangle
:
Find L:
L = 10 - 2.25
L = 7.75; length of the original rectangle
:
Length increased by 4 times the width
7.75 + 4(2.25) =
7.75 + 9 = 16.75; length of the new rectangle, Width remains at 2.25
:
What is its area?
New rectangle area;
16.75 * 2.25 = 37.6875
:
:
Check the sum of the dimensions of the new rectangle
16.75 + 2.25 = 19
