SOLUTION: The area of a rectangle is 48 square meters. The length of a diagonal is ten meters. Find the perimeter of the rectangle.

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Question 389086: The area of a rectangle is 48 square meters. The length of a diagonal is ten meters. Find the perimeter of the rectangle.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If you recall the 6-8-10 triangle, you can see that the length is 8 and the width is 6, and the perimeter is 28.

If not, we can observe that if x is the length and y is the width, then

sqrt%28x%5E2+%2B+y%5E2%29+=+10

x%5E2+%2B+y%5E2+=+100

We want to find 2(x + y). If we take x + y and square it, we obtain

%28x%2By%29%5E2+=+x%5E2+%2B+2xy+%2B+y%5E2. Note that x%5E2+%2B+y%5E2+=+100 and xy+=+48. Substituting, this becomes:

%28x%2By%29%5E2+=+100+%2B+2%2848%29+=+196

x%2By+=+14

The perimeter is 2(x+y) = 28. Isn't it nice that we didn't even have to solve for the length and the width to find the perimeter?