Question

Jim’s backyard is rectangular with dimensions of 75 feet by 120 feet. He is planning to designate part of the yard to plant a vegetable garden. The garden will be a similar rectangle, using a scale factor of 25. How much fencing will he need if he wants to enclose the garden on all four sides? He will need feet of fence.

Answer 1

He will need 15.6 feet of fence

Explanation:

Jim's back yard has the following dimensions;

Length=120 feet

Width=75 feet

The gardens dimensions can be calculated using the expression;

Length of garden=Length of back yard/scale factor

where;

Length of back yard=120 feet

Scale factor=25

replacing;

Length of garden=120/25

Length of garden=4.8 feet

Width of garden=Width of back yard/scale factor

where;

Width of back yard=75 feet

Scale factor=25

replacing;

Width of garden=75/25

Width of garden=3 feet

The gardens dimension are;

Garden width=3 feet

Garden length=4.8 feet

To get the length of the fence that will enclose all four sides, we calculate the perimeter of the garden;

Perimeter=2(length+width)

Perimeter=2(4.8+3)=15.6 feet

He will need 15.6 feet of fence