SOLUTION: The diagonal of a rectangle is 15 inches and the area is 50 square inches. Find the dimensions of the rectangle, correct to one decimal place.

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Question 823842: The diagonal of a rectangle is 15 inches and the area is 50 square inches. Find the dimensions of the rectangle, correct to one decimal place.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!

The diagonal creates two triangles, each with legs x and y. Pythagorean theorem relationship gives highlight_green%28x%5E2%2By%5E2=15%5E2%29, because the diagonal also becomes the hypotenuse of the two triangles.

The given area permits the equation highlight_green%28xy=50%29.

Various ways to continue, but take the area equation and solve for either x or y; substitute into the pythagorean theorem equation and solve for the present variable; and then solve for the other using the area xy equation.

To start, y=50%2Fx;
x%5E2%2B%2850%2Fx%29%5E2=15%5E2
x%5E2%2B2500%2F%28x%5E2%29-15%5E2=0
You WILL need to deal with solving for x%5E2 first!
Multiplying left and right by x%5E2,
x%5E4%2B2500-15%5E2%2Ax%5E2=0
x%5E4-225x%5E2%2B2500=0
x%5E2=%28225%2Bsqrt%28225%5E2-4%2A2500%29%29%2F%282%29
x%5E2=%28225%2Bsqrt%2840625%29%29%2F%282%29
----note: 40625=25*1625=25*25*65-------
x%5E2=%28225%2B25%2Asqrt%2865%29%29%2F%282%29
..
Actually, x%5E2=%28225%2B201.556%29%2F%282%29 OR x%5E2=%28225-201.556%29%2F%282%29
x%5E2=213.278 OR x%5E2=11.722
Finishing the value for x,
highlight%28x=14.6%29 OR highlight%28x=3.4%29------ not really comfortable with this level of accuracy expected, but you can recompute if you wanted this one.

You can take care of the value of y.