Math Question Grade 10

Question

Rebecca is building a fence at the side of her house. She has 120m of fencing and plans to use the side of the house as one side of the rectangular fenced area. What dimensions will give a maximum area? 

The answer my teacher gave was: 30m x 60m 

I want to know the steps in finding the answer. 

Thanks in advance. :)

Answer 1

Let l and w are the length and width of fence.

To get maximum area, consider the side of the house along the length of the fenced area.

Perimeter of the rectangle = 2 (l+ w)

Write the algebraic expression for the current situation.

2 (l+ w) = 120 + l

2l + 2w = 120 +l

l + 2w = 120

To solve the equation we need two equations. Since we don't have enough data assuming width of the area is half of the rectangle/fence length side = w = l/2

l + 2 * l/2 = 120

2l = 120

l = 60 m

Width = l/2 = 60/2 = 30m

Dimensions are l = 60 m and w = 30 m

I hope this helps...