posted by paukate08 .
a gardener is planning to make a rectangular garden with an area of 80ft^2.she has 12 yards of fencing to put around the perimeter of the garden.what should the dimension of the garden be ?
For a given perimeter, that largest area area of a rectangle is obtained when the rectangle is a square.
so if each side is x ft
x^2 = 80
x = √80 = 4√5
She needs 16√5 ft or appr 35.8 ft of fencing.
With only 12 feet she cannot have a rectangular field of 80 ft
with 12 ft of fencing , she can build a 3by3 square which will hold 9 square ft, not the 80 she wants.
Your question is flawed.
She has 12 yards, or 36 feet of fencing.
That will enclose 9x9 = 81 ft^2, so by moving away from a square, she can use the whole 36 ft to enclose only 80 ft^2.
80 = 16*5 = 4*(4*5) so if the garden is 8x10 feet, its perimeter is 36 and its area is 80
I violated one of the first rules I taught my students years ago ...
Read the question carefully, and read it more than once.