SOLUTION: what is the length and width of a rectangle with the given the given perimeter 19.9 cm here is the original question: The perimeter of a rectangle is about 19.9 cm. If

Algebra ->  Rectangles -> SOLUTION: what is the length and width of a rectangle with the given the given perimeter 19.9 cm here is the original question: The perimeter of a rectangle is about 19.9 cm. If       Log On


   

Question 937116: what is the length and width of a rectangle with the given the given perimeter 19.9 cm here is the original question: The perimeter of a rectangle is about 19.9 cm. If you double the width of the rectangle the perimeter is about 25.7 cm. Find the dimensions of the smaller rectangle. Round the given values to the nearest integer. Use the rounded values to write and solve a system of equations to find the length and the width of the rectangle.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Original rectangle: w for width, L for length.
Let p=19.9, the perimeter.

New rectangle: 2w for width and still L for length.
Let P=25.7, the perimeter of the newer, newer, BIGGER rectangle.
Notice different case levels for each rectangle perimeter.


EQUATIONS

system%282w%2B2L=p%2C2%2A2w%2B2L=P%29

Simplify the system to
system%282w%2B2L=p%2C4w%2B2L=P%29
The unknowns for which to solve are w and L. P and p are already known, given.

Elimination Method is a good way to begin handling the system.

4w%2B2L-%282w%2B2L%29=P-p
2w=P-p
highlight%28w=%28P-p%29%2F2%29, the symbolic result for width w.

Taking the simple system but multiplying first equation by 2,
system%284w%2B4L=2p%2C4w%2B2L=P%29
Now subtract the second equation from the first equation to eliminate w.
4w%2B4L-%284w%2B2L%29=2p-P
2L=2p-P
highlight%28L=%282p-P%29%2F2%29, symbolic result for length L.