# How To Solve The Dimension Of A Rectangle?

The product of the dimensions of a rectangle is the area. Usually questions asking about dimensions give you some relation between the dimensions and the area. You use the given information together with your knowledge of the area formula to create and solve the appropriate equations.

Example
Given: The length of a rectangle is 3 units more than the width. The area is 40 square units.
Find: What are the length and width?
Solution: Let "L" be the length, "W" be the width.
L = W + 3    (the length is 3 units more than the width)
L*W = 40    (the area is 40 square units)

The first equation provides an expression for L, so we can substitute that into the second equation to get an equation in W alone.
(W + 3)*W = 40
Now, we solve this.
W2 + 3W - 40 = 0    (multiply it out, subtract 40 from both sides)
(W+8)(W-5) = 0    (factor the expression)
W = -8 or W = 5    (identify values that make the factors =0)
We know the dimensions must be positive, so we choose the W = 5 solution. We also know that L=W+3, so that means L = 5+3 = 8
The length and width of the rectangle are 8 units and 5 units.

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Perimeter of Rectangle = 2(Length + Width)

Where Perimeter = 220 m
Width = w
Length = 2w-40
Putting the values in the equation you will get

220 = 2((2w-40)+w)
220 = 2(2w-40+w)
220 = 2(3w-40)
220 = 6w - 80
6w - 80 = 220
Adding 80 on both sides you will get

6w = 220+80
6w = 300

Dividing 6 on both sides you will get
6/6w = 300/6
w = 50

So width = 50m
Length = 2(50)-40
=100-40
= 60m

Length = 60 m
Width = 50 m
perimeter = 220m

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Use a ruler to measure the sides.
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Relate the information you are given about the rectangle to what you know about the relations involving rectangles. Write equations if necessary. Draw a picture, if that will help. Solve for the unknown.

Area = length*width
Perimeter = 2(length + width)
diagonal = √(length2 + width2)
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