SOLUTION: Consider two rectangles, A and B. Rectangle A is four times as long as rectangle B and three times as wide. The perimeter of rectangle A is 106 cm and the perimeter of rectangle B

Question 722578: Consider two rectangles, A and B. Rectangle A is four times as long as rectangle B and three times as wide. The perimeter of rectangle A is 106 cm and the perimeter of rectangle B is 30 cm.
What are the dimensions of the larger rectangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Consider two rectangles, A and B. Rectangle A is four times as long as rectangle B and three times as wide.
The perimeter of rectangle A is 106 cm and the perimeter of rectangle B is 30 cm.
What are the dimensions of the larger rectangle?
:
Let a = length of the small rectangle
then
4a = the length of the large rectangle
:
Let b = the width of the small rectangle
then
3b = the width of the large rectangle
:
" The perimeter of rectangle A is 106 cm"
2(4a) + 2(3b) = 106
simplify, divide by 2
4a + 3b = 53
:
"the perimeter of rectangle B is 30 cm."
2a + 2b = 30
simplify, divide by 2
a + b = 15
b = (15-a)
:
Replace b with (15-a) in the 1st perimeter equation
4a + 3(15-a) = 53
4a + 45 - 3a
4a - 3a = 53 - 45
a = 8 cm is the length of the small rectangle
and
b = 15-8
b = 7 cm is the width of the small rectangle
:
"What are the dimensions of the larger rectangle?
4(8) = 32 cm is the length
3(7) = 21 cm is the width
:
:
See if the that checks out, find the perimeter with these values
2(32) + 2(21) =
64 + 42 = 106
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