SOLUTION: If the diagonal of a rectangle has a length 7 feet and the rectangles area is 16 square feet find the number of feet in the rectangles perimeter

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Question 935684: If the diagonal of a rectangle has a length 7 feet and the rectangles area is 16 square feet find the number of feet in the rectangles perimeter
Found 3 solutions by ankor@dixie-net.com, josgarithmetic, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If the diagonal of a rectangle has a length 7 feet and the rectangles area is 16 square feet
let x = the width, let y = the length
Two equations
x^2 + y^2 = 7^2
y^2 = 49 - x^2
y = sqrt%2849-x%5E2%29
and
xy = 16
y = 16%2Fx
Graph these two equations
+graph%28+300%2C+200%2C+-6%2C+10%2C+-10%2C+10%2C+16%2Fx%2C+sqrt%2849-x%5E2%29%29+
they intersect; x=2.44, y=6.56 and x=6.56, y=2.44
length = 6.56 ft
width = 2.44 ft
:
find the rectangles perimeter
2(6.56) + 2(2.44) = 18 ft

Answer by josgarithmetic(39617) About Me  (Show Source):
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The diagonal of the rectangle is a hypotenuse for each of the two triangles that it forms.

x and y, length and "width",
system%28x%5E2%2By%5E2=7%5E2%2Cxy=16%29

y=16%2Fx, substitute this.
x%5E2%2B%2816%2Fx%29%5E2=49
x%5E4%2B16=49x%5E2
x%5E4-49x%5E2%2B16=0, quadratic form.

x%5E2=%2849%2Bsqrt%2849%5E2-4%2A16%29%29%2F2
x%5E2=%2849%2Bsqrt%282337%29%29%2F2
2337=3*779=3*19*41
Computing into base-ten values,
highlight%28x=sqrt%28%2849%2Bsqrt%282337%29%29%2F2%29%29
x=0.328736 and y=48.671264
--
Perimeter would be highlight%282%280.328736%2B48.671264%29%29, and you can choose what accuracy you want, or recalculate x and y to greater accuracy and use that if you want.


The quadratic form equation found in x would be the same if found in y, so the PLUS_OR_MINUS forms of the general solution method will give separately the x and the y. Both are found and understood as positive values.

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

If the diagonal of a rectangle has a length 7 feet and the rectangles area is 16 square feet find the number of feet in the rectangles perimeter 
Perimeter of rectangle: highlight_green%2818%29 feet

You can do the check!! 

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