SOLUTION: A rectangle with an area of 32 inches squared has one side measuring 4 inches. A similar rectangle has an area of 288 inches squared. How long is the longer side in the larger re

Algebra ->  Surface-area -> SOLUTION: A rectangle with an area of 32 inches squared has one side measuring 4 inches. A similar rectangle has an area of 288 inches squared. How long is the longer side in the larger re      Log On


   

Question 157158: A rectangle with an area of 32 inches squared has one side measuring 4 inches. A similar rectangle has an area of 288 inches squared. How long is the longer side in the larger rectangle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If they are similar, then l%5B1%5D%2Fw%5B1%5D+=+l%5B2%5D%2Fw%5B2%5D
A%5B1%5D+=+l%5B1%5D%2Aw%5B1%5D
32+=+l%5B1%5D%2A4
l%5B1%5D+=+8in
---------------------
A%5B2%5D+=+l%5B2%5D%2Aw%5B2%5D
288+=+l%5B2%5D%2Aw%5B2%5D
l%5B2%5D+=+288%2Fw%5B2%5D
---------------------
l%5B1%5D%2Fw%5B1%5D+=+l%5B2%5D%2Fw%5B2%5D
8%2F4+=+l%5B2%5D%2Fw%5B2%5D
2+=+%28288%2Fw%5B2%5D%29%2Fw%5B2%5D
multiply both sides by w%5B2%5D
2w%5B2%5D+=+288%2Fw%5B2%5D
multiply both sides by w%5B2%5D again
2w%5B2%5D%5E2+=+288
w%5B2%5D%5E2+=+144
w%5B2%5D+=+12
l%5B2%5D+=+288%2Fw%5B2%5D
l%5B2%5D+=+288%2F12
l%5B2%5D+=+24 in answer
Check:
288+=+l%5B2%5D%2Aw%5B2%5D
288+=+24%2A12
288+=+288
OK