The length of a rectangular parking lot is 10 meters less than twice its width, and the perimiter is 412 meters, find the length of the parking lot.

Question

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Answer 1

We know that Perimeter = 2 times the Length + 2 times the Width

 

So, L = 2W - 10m, and P = 412m

 

Our equation becomes 2(2W -10m) + 2W = 412m

expanding the equation, we get 4W - 20m + 2W = 412m

which becomes 6W = 432m

W = 72m

therefore, L = 2W -10m = 2(72m) - 10m = 134m

 

Proof: P = 2L + 2W = 2(134m) + 2(72m) = 412m

Answer 2

A rectangle is quadrilateral that has two pairs of parallel sides.  The perimeter of any shape is the sum of the exterior sides.

 

Perimeter = 2L + 2w

 

where:
L = length
w = width

 

 

Let width = x

Let length = 2x - 10

Perimeter = 412 meters

 

where:

L=length

w=width

 

Set up equation for perimeter using the variables.

 

2x + 2(2x - 10) = 412

2x + 4x - 20 = 412

6x - 20 = 412

6x = 432

  x = 72

 

Substitute this value of x into the variable of length.

 

length = 2(72) - 10 = 144 - 10 = 134

 

The length of the rectangle is 134 meters.