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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