Jose needs a rectangular section of his yard. The perimeter of the section is 27 feet, and the area is 35 square feet. Find the length and width of the section?

Question

anonymous · Answer

Perimeter of a rectangle = 2x + 2y = 27.  (1)
Area = xy = 35.
So x = 35/y. Sub this into (1) to find y.

anonymous · Answer

Can you write an equation for the perimeter of the section?

anonymous · Answer

the perimeter is 2(length) + 2(width) = 27.

anonymous · Answer

Using L and W, write an equation for the area of the section?

anonymous · Answer

That was the second equation, A = xy = 35.

anonymous · Answer

How do you solve for W?

mathstudent55 · Answer

Let length = L
Let width = W
P = 2L + 2W
A = LW

2L + 2W = 27
LW = 35
Solve area equation for L:
L = 35/W
Substitute into perimeter equation:
2(35/W) + 2W = 27
70/W + 2W = 27
Multiply both sides by W:
70 + 2W^2 = 27W
2W^2 - 27W + 70 = 0
(2W - 7)(W - 10) = 0
2W - 7 = 0 or W - 10 = 0
2W = 7 or W = 10
W = 7/2 or W = 10
Since we want the width to be smaller than the legth, we choose W = 7/2 as our answer.
W = 3.5, L = 10
width = 3.5 ft; length = 10 ft