A Square has its length and width increase by 2 feet and 4 feet respectively so that it is now a rectangle. The perimeter of the new rectangle is 8 feet less than twice the original perimeter. What was the original perimeter? Show I'll work the leads answer

Question

Krish Hood

Mathematics

2 February, 06:42

A Square has its length and width increase by 2 feet and 4 feet respectively so that it is now a rectangle. The perimeter of the new rectangle is 8 feet less than twice the original perimeter. What was the original perimeter? Show I'll work the leads answer

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Answers (1)

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Sexton · Answer 1

Step-by-step explanation:

Let L represent the length of one side of the square.

A Square has its length and width increase by 2 feet and 4 feet respectively so that it is now a rectangle. This means that the length of the new rectangle would be L - 2 and its width would be L - 4

The perimeter of the original square is 4L.

The perimeter of the new rectangle is 8 feet less than twice the original perimeter. This means that

2[ (L - 2) + (L + 4) = 4L * 2 - 8

2 (L - 2 + L + 4) = 8L - 8

4L + 4 = 8L - 8

8L - 4L = 4 + 8

4L = 12

L = 12/4 = 3

The original perimeter of the square is

3 * 4 = 12 feet