SOLUTION: The lengths of the sides of three squares are x, x+1, and x+2.If their total area is 365 m^2, find their total perimeter.

Algebra ->  Points-lines-and-rays -> SOLUTION: The lengths of the sides of three squares are x, x+1, and x+2.If their total area is 365 m^2, find their total perimeter.      Log On


   



Question 178710: The lengths of the sides of three squares are x, x+1, and x+2.If their total area is 365 m^2, find their total perimeter.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the sides of the 3 squares are
x, x%2B1, and x%2B2,
their areas are:
x%5E2, %28x%2B1%29%5E2, and x%2B2%29%5E2
given:
The total area of the 3 squares is 365 m2
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x%5E2+%2B+%28x%2B1%29%5E2+%2B+%28x%2B2%29%5E2+=+365
x%5E2+%2B+x%5E2+%2B+2x+%2B+1+%2B+x%5E2+%2B+4x+%2B+4+=+365
3x%5E2+%2B+6x+%2B+5+=+365
3x%5E2+%2B+6x+-+360+=+0
x%5E2+%2B+2x+-+120+=+0
Solve by completing the square
x%5E2+%2B+2x+%2B+%282%2F2%29%5E2+=+120+%2B+%282%2F2%29%5E2
x%5E2+%2B+2x+%2B+1+=+121
%28x+%2B+1%29%5E2+=+11%5E2
x+%2B+1+=+11
x+=+10
x%2B1+=+11
x%2B2+=+12
If the side of a sqare = s, then
the perimeter = 4s, so the perimeters are:
4x+=+40
4%2A%28x%2B1%29+=+44
4%2A%28x%2B2%29+=+48
40+%2B+44+%2B+48+=+132m