SOLUTION: I need help on finding the dimensions of a rectangle on this problem. Two rectangles are similar. The perimeter of the smaller rectangle is 72 inches and the perimeter of the lar

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Question 946746: I need help on finding the dimensions of a rectangle on this problem.
Two rectangles are similar. The perimeter of the smaller rectangle is 72 inches and the perimeter of the larger rectangle is 216 inches. If the width of the smaller rectangle is 12 inches, what are the dimensions of the larger triangle?
A. 18 inches by 90 inches
B. 36 inches by 72 inches
C. 36 inches by 60 inches
D. 24 inches by 84 inches
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I thought about this and I could not understand, but I do understand that if I get the area of the options (a,b,c,d) the found the scale factor, I could multiply by the original rectangle and see which option would give me my larger squares perimeter of 216.
Found 2 solutions by josgarithmetic, addingup:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The two rectangles are similar so their corresponding linear values are in proportion. The ratio
of the big to small rectangles' linear dimensions is 216%2F72=54%2F18=18%2F6=highlight_green%283%29.

Use this to find the width for the big rectangle.
W%2F12=3%2F1
W=3%2A12
highlight_green%28W=36%29


Now you know:
Big Rectangle,
perimeter 216
Width 36
Length ---- You can now find this because you know the perimeter.

2%2A36%2B2%2AL=216, using perimeter formula
36%2BL=108
L=108-36
highlight%28L=72%29

SUMMARY: Length 72, Width 36, for the big rectangle.


This part could be done also but is not necessary, and was not asked:
Let w and L width and LENGTH of the small rectangle.
-
36%2Fw=3
w%2F36=1%2F3
w=36%2F3
highlight%28w=18%29
-
You know the perimeter as given.
2%2A18%2B2%2AL=72
18%2BL=36
L=36-18
highlight%28L=12%29

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter (P)= 2H+2W (2 Height + 2 Widths)and we have:
P= 72 and W= 12
72 = 2(12)+ 2x
72 = 24 + 2x subtract 24, both sides
72-24= 24-24+2x
48 = 2x Now divide both sides by 2:
48/2 = 2x/2
24 = x, though it's more mathematically elegant to express: x = 24.
Proof: 24+24+12+12 = 72
Now let's go for the bigger rectangle. it's similar. The small rectangle has a 1:2 ratio on the length of its sides (12 wide by 24 high, 24 is = 12 x 2)Look quickly at the options they've given you:Do you see any two numbers where one is exactly double the other? I see 36 x 72, it's the only set among your choices where one number is double the other number. And 36+36+72+72 = 216, so this is your answer. Now, if you have to prove it:
P= 216
216 = x+x+2x+2x (1:2 ratio)Add the x:
216 = 6x Divide both sides by 6:
216/6 = 6x/6
36 = x, or x= 36 And the other side is 36 x 2 = 72