A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft2

Question

A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 1875 ft²

^{in feet? (larger dimension)}

^{width in feet (smaller dimension)}

Answer 1

What are we being asked to find?

length and width

What are we given?

area is 1875 ft

rectangular

Perimeter is 200ft.

What do we know that could apply?

Area = length X width

Perimeter = 2 X length + 2 X width 

Draw a visual, and label it.

Write an algebraic model:

1875 = l X w

200 = 2l + 2w

Two equations with unknowns

Use one equation to define l in terms of w and substitute the result into the other equation.

(200 - 2w) / 2 = l

1875 = (200 - 2w) / 2 X w

Solve for w, then substitute the result into either one of the original equations to solve for l .

Note the process:

A. What is being asked?

B. What are we given?

C. Map out a visual and label

D. What do we already know from past learning that is relevant?

E.1. Figure out how to manipulate all the resultant relationships to find the answer; and

E.2. if you don't know what to do, start doing something that you do know can be done, and see where it takes you.

G. Did you answer the question being asked?

H Is your answer reasonable.

Use this process for everything.