SOLUTION: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

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Question 283279: Rectangular stage. One side of a rectangular stage is
2 meters longer than the other. If the diagonal is 10 meters,
then what are the lengths of the sides?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The Pythagorean theorem applies: the diagonal is the hypotenuse of a right triangle.
The sides are the triangle are the length and width of the rectangle.
We are told the diagonal is 10 m.
.
L+=+length
W+=+width
L+=+W%2B2 :: The length is 2 m > width, so the width + 2 = length
.
L%5E2+%2B+W%5E2+=+10%5E2
.
substitute L+=+W%2B2
.
%28W%2B2%29%5E2+%2B+W%5E2+=+100
.
W%5E2+%2B+4W+%2B+4+%2B+W%5E2+=+100
.
2W%5E2+%2B+4W+-+96+=+0
.
divide through by 2
.
W%5E2+%2B+2W+-48+=+0
.
factor
.
%28W%2B8%29%28W-6%29=+0
.
So our choices are W=-8 and W=6, but a negative width doesn't make sense.
.
L+=+W%2B2+=+6%2B2+=+8
.
checking our solution, is the diagonal 10?
.
6%5E2%2B+8%5E2+=+36+%2B+64+=+100
.
So the diagonal+=+sqrt%28100%29=10
Correct
.
Answer:
The lengths of the sides of the rectangle are 6 and 8.
.
Done.