My rectangle has a 180mm perimeter, the width is half the length. What is the area?

Question

I want an explanation, let 'L' be length and 'W' be width.

Answer 1

The variable W represent the width of the rectangle and the variable L represent the length of the rectangle.

Since the width is one half of the length, we can write:

L = 2W

Also perimeter is equal to 2 times the length plus 2 times the width, so we can write:

P = 2L + 2W

We can substitute 2W for L and write:

P = 2 (2W) + 2W

Since the perimeter is 180 mm, we can write:

180 = 4W + 2W

This is equivalent to 180 = 6W

We can divide both sides of the equation by 6 and determine W:

180 = 6W

180/6 = 6W/6

30 mm = W

The length, L, will be 2W or 2 * 30 = 60mm

We can find the area by multiplying the length times the width:

A= L * W

A = 60 * 30

A =1800 Square mm