SOLUTION: The length of a rectangle is 2 cm more than three times the width. Find the dimensions of this rectangle if the area is 21 cm^2. I found the answer by trial and error (9 & 2 1/3

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Question 275915: The length of a rectangle is 2 cm more than three times the width. Find the dimensions of this rectangle if the area is 21 cm^2.
I found the answer by trial and error (9 & 2 1/3) but I need to know how to actually figure it out and show work. Is there another way besides just plugging in numbers? Thank you!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 2 cm more than three times the width.
Find the dimensions of this rectangle if the area is 21 cm^2.
:
There is, and it's pretty easy
:
Write an equation for each statement
"The length of a rectangle is 2 cm more than three times the width."
L = 3W + 2
and
" the area is 21 cm^2. "
L * W = 21
:
Replace L with (3W+2) from the 1st statement
(3W + 2) * W = 21
3W^2 + 2W - 21 = 0
A quadratic equation we can factor
(3W - 7)(W + 3) = 0
The positive solution
3W = 7
W =
W = 2 is the width
:
Find the length using L = 3W + 2
L = 3() + 2
L = 7 + 2
L = 9
;
:
Check solutions by finding the area
9 * = 21