SOLUTION: the diagonal and the longer side of a rectangular plot are together three times the length of the shorter side, if the longer side exceeds the shorter side by 120 feet, what is the

Algebra ->  Rectangles -> SOLUTION: the diagonal and the longer side of a rectangular plot are together three times the length of the shorter side, if the longer side exceeds the shorter side by 120 feet, what is the      Log On


   

Question 930973: the diagonal and the longer side of a rectangular plot are together three times the length of the shorter side, if the longer side exceeds the shorter side by 120 feet, what is the area of the plot?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
d for diagonal; y and x the sides, y is longer side.

d+y=3x; y-x=120.
x and y also form two right triangles since x and y form a rectangle.
x^2+y^2=d^2.

System:
system%28d%2By=3x%2Cy-x=120%2Cx%5E2%2By%5E2=d%5E2%29
More than one way to go to solve the system, but you are mostly interested in x and y. The area will be xy.

Try focusing first on eliminating d from the quadratic equation and then eliminate either x or y from the quadratic equation:
d=3x-y from first equation.
x%5E2%2By%5E2=%283x-y%29%5E2 when substituted.
x%5E2%2By%5E2=9x%5E2-6xy%2By%5E2
Notice y%5E2 is shown on both sides.
x%5E2=9x%5E2-6xy
0=8x%5E2-6xy
highlight_green%284x%5E2-3xy=0%29
Now, use the second equation of the system to eliminate y in this simplified quadratic equation, and solve for x.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

the diagonal and the longer side of a rectangular plot are together three times the length of the shorter side, if the longer side exceeds the shorter side by 120 feet, what is the area of the plot?
Area of plot: highlight_green%28172800%29 ft2

You can do the check!! 

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