SOLUTION: Rose is carefully framing a 12-inch x 16-inch family photo so that the length and width of the frame have the same ratio as the photo. She is using a piece of frame 70 inches in le

Algebra ->  Rectangles -> SOLUTION: Rose is carefully framing a 12-inch x 16-inch family photo so that the length and width of the frame have the same ratio as the photo. She is using a piece of frame 70 inches in le      Log On


   

Question 917664: Rose is carefully framing a 12-inch x 16-inch family photo so that the length and width of the frame have the same ratio as the photo. She is using a piece of frame 70 inches in length (perimeter). What are the length and width of the frame?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +L+ = length of the frame
Let +W+ = the width of the frame
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Given:
+L%2FW+=+16%2F12+
(1) +L%2FW+=+4%2F3+
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+P+=+2L+%2B+2W+ ( formula )
+70+=+2L+%2B+2W+
(2) +35+=+L+%2B+W+
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(1) +L+=+%284%2F3%29%2AW+
Substitute this into (2)
(2) +35+=+%284%2F3%29%2AW+%2B+W+
(2) +35+=+%287%2F3%29%2AW+
(2) +W+=+%283%2F7%29%2A35+
(2) +W+=+15+
and, since
(2) +L+%2B+W+=+35+
(2) +L+=+35+-+15+
(2) +L+=+20+
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The length is 20 in.
The width is 15 in.
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check:
+L%2FW+=+16%2F12+
+20%2F15+=+16%2F12+
+4%2F3+=+4%2F3+
OK