Question

A rectangular lot whose perimeter is 260 ftis fenced along three sides. An expensive fencing along the​ lot's length cost $ 18per foot. An inexpensive fencing along the two side widths costs only $ 3per foot. The total cost of the fencing along the three sides comes to $ 1800.What are the​ lot's dimensions?

Answer 1

Lot's dimension is 68 ft x 96 ft

Step-by-step explanation:

A rectangular lot whose perimeter is 260 ft is fenced along three sides. An expensive fencing along the​ lot's length cost $ 18per foot. An inexpensive fencing along the two side widths costs only $ 3per foot.

So we have

         l + 2 w = 260 -------------------eqn 1

And total cost is 1800 $

That is

                18 l + 2 x 3 w = 1800

                 3l + w = 300 -------------------eqn 2

eqn 2 x 2

                 6l + 2w = 600 -------------------eqn 3

eqn 3 - eqn 1

              6l + 2w - l - 2w = 600 - 260

                   5l = 340

                     l = 68 ft

Substituting in eqn 1        

                   68 + 2 w = 260    

                     2w = 192

                       w = 96 ft

Lot's dimension is 68 ft x 96 ft