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the length of a rectangle is 8 meters more than twice its width. the perimeter is 112 meters. find it's area

Sagot :

Glendzmoralesidn

Answer:

The area of the rectangle is 640 square units.

Step-by-step explanation:

First, translate the English sentence to Mathematical sentence for the length of the rectangle.

It states that the length of a rectangle is 8 meters more than twice its width, giving an equation of:

L = 8 + 2W       equation 1

Then, translate also the English statement of the perimeter to Mathematical sentence.

It states that the perimeter is 112. But the formula for a perimeter is:

P = 2L + 2W     equation 2

112 = 2L + 2W

By using Substitution method, substitute equation 1 to equation 2:

112 = 2(8 + 2W) + 2W

112 = 16 + 4W + 2W

112 = 16 + 6W

W = [tex]\frac{112-16}{6}[/tex]

W = 16

Then substitute W = 16 to equation 1, we get:

L = 8 + 2W

L = 8 + 2(16)

L = 40      

Therefore, to get the area of the rectangle, we use he formula:

A = L x W

A = 40 x 16

A = 640 sq. units

Therefore, the area of the rectangle is 640 sq. units

For additional readings about this topic, you can click from the following links:

* How to find the area of a rectangle

  https://brainly.ph/question/110308

* Anther example for finding the area of a rectangle

  https://brainly.ph/question/2004152

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