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.

He will need 15.6 feet of fence

Step-by-step 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