SOLUTION: a rectangle has an area of 132 cm ^2 and a perimeter of 56 cm. find the dimensions of the rectangle

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Question 863487: a rectangle has an area of 132 cm ^2 and a perimeter of 56 cm. find the dimensions of the rectangle
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
let x = a dimension of a rectangle
let y = the dimension of a rectangle at right angle to x
let p = perimeter
let A = area
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Formula for rectangle perimeter: p=2%28x%2By%29
Formula for area of a rectangle: xy=A

Assuming the given variables are p, A, and the unknown variables x and y and these need to be solved,
y=A%2Fx.
Substitute into perimeter equation;
p=2%28x%2B%28A%2Fx%29%29
2%28x%5E2%2BA%29%2Fx=p
2%28x%5E2%2BA%29=px
2x%5E2%2B2A=px
highlight_green%282x%5E2-px%2B2A=0%29----- This is only part way to the completed solution.
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Note certain things:

This is a quadratic equation, still in symbolic form;
A formula for x can be solved using the general solution to a quadratic equation;
If you substitute the given values NOW, you will probably learn that the quadratic expression will be factorable;
You still need to solve for y.