Question

You are enclosing a rectangular garden with 180 feet of omamental fencing. The area of the garden is 1800 square feet. What are the dimensions of the garden?

Answer 1

Answer:

Step-by-step explanation:

Perimeter is

P = 2L + 2W.  We are given the perimeter as 180 feet, so

180 = 2L + 2W.  Solve this for either L or W.  I chose W, no reason...

180 - 2L = 2W so

90 - L = W  Hold that thought.  We'll come back to it in a minute.

Area is

A = LW.  We are given the area as 1800 square feet, so

1800 = LW.  Sub in 90 - L for W:

1800 = L(90 - L).  Distribute to get a quadratic:

$1800=90L-L^2$

Get everything on one side and solve for the length by factoring:

$-L^2+90L-1800=0$

Factor this however you like to factor quadratics, to get the length of

L = 30 and L = 60.  First off, the length is longer than the width in general, so if we want to solve for the width, plug in 60 as L in the equation in bold print:

90 - 60 = W and

30 = W

So L = 60 and W = 30