SOLUTION: The length of a rectangle is 3 times the width. The perimeter of the rectangle is equal to the perimeter of a triangle that has one side equal to the length of the rectangle. The s
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Question 528560: The length of a rectangle is 3 times the width. The perimeter of the rectangle is equal to the perimeter of a triangle that has one side equal to the length of the rectangle. The sum of the other 2 sides of the triangle equals 85. What is the length and width of the rectangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let the three sides of the triangle be; a, b, c
:
Write an equation for each statement.
:
The length of a rectangle is 3 times the width.
L = 3W
:
The perimeter of the rectangle is equal to the perimeter of a triangle
2L + 2W = a + b + c
:
that has one side equal to the length of the rectangle.
a = L
:
The sum of the other 2 sides of the triangle equals 85.
b + c = 85
:
2L + 2W = a + b + c
Replace a with L, replace b+c with 85
2L + 2W = L + 85
2L - L + 2W = 85
L + 2W = 85
Replace L with 3W
3W + 2W = 85
5W = 85
W = 85/5
W = 17 is the width of the rectangle
then
3(17) = 51 is the length of the Rectangle
:
You should confirm this by finding the actual perimeter of the rectangle and the triangle.
2(51) + 2(17) = 51 + 85
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