Question

Anna has a 25-meter-long fence that she plans to use to enclose a rectangular garden of width w. The fencing will be placed around all four sides of the garden so that its area is 25 square meters
Write an equation in terms of w that models the situation.

Answer 1

Answer:

w^2-12.5w+25=0

Step-by-step explanation:

P=2L+2W

25=2L+2W

12.5=L+W

L=12.5-12

A=LW

25=(12.5-W)W

25=12.5W-W^2

-W^2+12.5W-25=0

W^2-12.5w+25=0

Answer 2

Answer:   -2w^2 + 25w = 25    or    -2w^2 + 25w - 25 = 0

================================================================

Explanation:

Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.

The area of the rectangle is

Area = length*width

Area = L*W

Area = (25-2w)*w

Area = 25w - 2w^2

Area = -2w^2 + 25w

Set this equal to the desired area (25 square meters) to get

-2w^2 + 25w = 25

and we can subtract 25 from both sides to get everything on one side

-2w^2 + 25w - 25 = 0

side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)