SOLUTION: Rectangles A and B are both four times as long as they are wide and the length of rectangle A is three times the length of rectangle B. If the difference in the perimeters is 16cm,

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Question 1172906: Rectangles A and B are both four times as long as they are wide and the length of rectangle A is three times the length of rectangle B. If the difference in the perimeters is 16cm, find the dimensions of each rectangle.
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Rectangles A and B are both four times as long as they are wide
and the length of rectangle A is three times the length of rectangle B.
If the difference in the perimeters is 16cm, find the dimensions of each rectangle.
:
let w = width of rectangle B
then
4w = the length of rectangle B
And
3(4w) = 12w = the length of rectangle A
3w = the width of rectangle A, (1/4th of A's length)
:
2(12w + 3w) - 2(4w + w) = 16
simplify, divide equation by 2
(12w + 3w) - (4w+w) = 8
15w - 5w = 8
10w = 8
w = 8/10
w = .8 cm is the width of rectangle B
and
4(.8) = 3.2 cm is length of rectangle B
then
3(.8) = 2.4 cm is width of rectangle A
and
4(2.4) = 9.6 is length of rectangle B
:
:
see if this checks out
2(9.6 + 2.4) - 2(3.2 + .8) =
2(12) - 2(4) =
24 - 8 = 16
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Rectangles A and B are both four times as long as they are wide.
They are similar (have the same shape)

Let w = the small rectangle's width.
Then 4w = the small rectangle's length.
the length of rectangle A is three times the length of rectangle B
Since 4w = the small rectangle's length,
3(4w) or 12w = the length of the large rectangle's length.

Since the rectangles are similar, the width of the larger triangle is
also three times the width of the smaller rectangle.

So 3w = the width of the larger rectangle.
If the difference in the perimeters is 16cm,

The formula for the perimeter is 


  










So the width of the smaller rectangle B is 4/5 = 0.8 cm

4w = the small rectangle's length = 4(4/5) = 16/5 - 3.2 cm

3w = the width of the larger rectangle = 3(4/5) = 12/5 = 2.4 cm

12w = the length of the large rectangle's length = 12(4/5) = 48/5 = 9.6 cm





Edwin
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