The perimeter of a rectangle is 36m. If the width were doubled and the length increased by 13m, the perimeter would be 74m. What are the length and width of the rectangle?

Answer 1

In short the answer is the width = 6 and the length = 12.

Explanation:

You can solve this by creating equations. Let L stand for length and W for width. The original rectangle can be represented by the equation

2L + 2W = 36

The second rectangle can be represented by the equation

2(L+13) + 2(2W) = 74

simplifying we get

2L + 26 + 4W = 74

subtracting 26 from each side we get

2L + 4W = 48

This is a system of equations, which can be solved by subtracting the second equation from the first, which will cancel out the 'L' variable. If we do this, we get

-2W = -12

so W = 6

Plugging back into the first equation to solve for L:

2L + 2(6) = 36

2L + 12 = 36

2L = 24

L = 12