SOLUTION: The length of a rectangle is two feet less than three times width of The length of a rectangle is two feet less than three times width of the rectangle . The area of the reactangl

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Question 885556: The length of a rectangle is two feet less than three times width of
The length of a rectangle is two feet less than three times width of the rectangle . The area of the reactangle is 65ft. ?
a.) How would you represent the dimensionof the rectangle ?
b.) What equation represent the area of rectangle ?
c.) how will you find the dimension of the rectangle ?
d.)What are dimension of the rectangle?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
All your questions depend on finding the length and width of the rectangle.

Let w = width
Let L = length
wL=65, from description;
L=-2%2B3w, from description.

wL=w%283w-2%29=65
3w%5E2-2w=65
highlight_green%283w%5E2-2w-65=0%29

Is that factorable? Use trial and check or use discriminant.
Discriminant, %28-2%29%5E2-4%2A3%28-65%29=784
sqrt%28784%29=28------"Nice" whole number, so the quadratic in w is factorable.
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Try finding factorization:
(3w____13)(w____5)--------gives 13 and 15. You want negative 5....
highlight_green%28%283w%2B13%29%28w-5%29=0%29.
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The meaningful solution there is highlight%28w=5%29

Back to the description's definition for length L,
L=3w-2
L=3%2A5-2
highlight%28L=13%29.

You have what you need to answer your four questions.