SOLUTION: A rectangle has an area of 43.56 cm2. When both the length and width of the rectangle are increased by 1.20 cm, the area of the rectangle becomes 63.84 cm2. Calculate the length of

Algebra ->  Rectangles -> SOLUTION: A rectangle has an area of 43.56 cm2. When both the length and width of the rectangle are increased by 1.20 cm, the area of the rectangle becomes 63.84 cm2. Calculate the length of      Log On


   

Question 827529: A rectangle has an area of 43.56 cm2. When both the length and width of the rectangle are increased by 1.20 cm, the area of the rectangle becomes 63.84 cm2. Calculate the length of the shorter of the two sides of the initial rectangle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try assigning variables to everything.

x = length
y = width
A = 43.56 cm^2
B = 63.84 cm^2
c = 1.20 cm length increment to obtain B area

Form equations.

xy=A, and %28x%2Bc%29%28y%2Bc%29=B.
'
y%2Bc=B%2F%28x%2Bc%29
y=B%2F%28x%2Bc%29-c
y=B%2F%28x%2Bc%29-c%28x%2Bc%29%2F%28x%2Bc%29
y=%28B-cx-c%5E2%29%2F%28x%2Bc%29
'
Original area equation, A,
xy=A
x%28%28B-cx-c%5E2%29%2F%28x%2Bc%29%29=A
x%28B-cx-c%5E2%29=A%28x%2Bc%29
Bx-cx%5E2-c%5E2%2Ax=Ax%2BAc
-Bx%2Bcx%5E2%2Bc%5E2%2Ax=-Ax-Ac
cx%5E2%2Bc%5E2%2Ax%2BAx-Bx=-Ac
cx%5E2%2Bc%5E2%2Ax%2BAx-Bx%2BAc=0
highlight%28cx%5E2%2B%28c%5E2%2BA-B%29x%2BAc=0%29

The time required to enter all of that as text and put in the rendering brackets is very long. Solve the quadratic equation for x and use the given values according to you best comfort to get a value for x; and use it to find y.
-
Note that you might want to compute the coefficients of the constant term, of x^2, and of x; before using the general solution to quadratic equation.
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I did NOT assume any convenience with the given numeric values.

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

A rectangle has an area of 43.56 cm2. When both the length and width of the rectangle are increased by 1.20 cm, the area of the rectangle becomes 63.84 cm2. Calculate the length of the shorter of the two sides of the initial rectangle.


Quadratic equation formed: L%5E2+-+15.7L+%2B+43.56+=+0, with L being the original length of the rectangle

Using the quadratic equation formula, dimensions are: 12.1 cm by 3.6 cm, which makes the shorter side: highlight_green%283.6%29 cm 

You can do the check!! 



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