SOLUTION: the length of a rectangle is 5cm. greater than twice its width. if the perimeter is 52 cm., what is the dimensions of the rectangle?

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Question 287100: the length of a rectangle is 5cm. greater than twice its width. if the perimeter is 52 cm., what is the dimensions of the rectangle?
Answer by sharon1948(6) About Me  (Show Source):
You can put this solution on YOUR website!
Problem #287100
1. the length of a rectangle is 5cm. greater than twice its width. if the perimeter is 52 cm., what is the dimensions of the rectangle
2. Let w=width
2w+5= length
I am a visual person so I draw the rectangle out and label it.
Next write the formula of the Area of a rectangle.
A=lw
With the information you have,replace it into the formula:
52=(2w+5)w (I rewrite the formula for my understanding)
w(2w+5)=52
Next we need to factor the equation and set it to equal 0:
2w^2 +5w=52
subtract 52 from the right and rewrite the equation:
2w^2+5w-52=0
Solve by grouping
2w^2+13w ] [ -8w -52 =0
w(2w+13) -4(2w+13) =0
(w-4) (2w+13)
Width = 4
Check:
52= ((2)4+5)4
52= (13)4
52=52
Length = 13
The dimensions of the rectangle are width equals 4cm and the length equals 13cm.