SOLUTION: the length of a rectangle is 13 centimeters less than six times its width. it's area is 15 square centimeters. find the dimensions of the rectangle.

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Question 949113: the length of a rectangle is 13 centimeters less than six times its width. it's area is 15 square centimeters. find the dimensions of the rectangle.
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
W=width; L=length=6W-13 cm;A=L*W=15 sq cm
A=L*W
15 sq cm=L*W Substitute for L.
15 sq cm=(6W-13)(W)
Subtract 15 sq cm from each side.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=529 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -0.833333333333333. Here's your graph:

The answer we want is 3 ANSWER: Width is 3 cm.
L=6W-13=6(3)-13=18-13=5 cm ANSWER: Length is 5 cm.
CHECk:
A=L*W
15 sq cm=5 cm*3 cm
15 sq cm=15 sq cm
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