Answer:
12 ft long by 5½ ft wide
Step-by-step explanation:
1. Set up an expression for the area.
Let l = the length of the rectangle
and w = the width. Then
2w = twice the width and
2w + 1 = 1 more than twice the width. Then
l = 2w + 1
The formula for the area of a rectangle is
A = length × width
A = lw
66 = (2w +1)w
66 = 2w² + w
2w² + w - 66 = 0
2. Solve the quadratic for w
2w² + w - 66 = 0
(a) Multiply the first and last terms
2 × (-66) = -132
(b) List all the factors of 132
1 132
2 66
3 42
4 33
6 22
11 12
(c) Find a pair of factors whose product is -132 and whose sum is 1.
After some trial and error, you will choose -11 and +12,
-11 × 12 = -132 and -11 + 12 = 1.
(d) Rewrite w as -11w + 12w
2w² - 11w + 12w - 66 = 0
(e) Factor by grouping
w(2w - 11) + 6(2w - 11) = 0
(w + 6)(2w - 11) = 0
(f) Use the zero product theorem
w + 6 = 0 2w - 11 = 0
w = -6 2w = 11
w = 5½
We reject the negative answer, so w = 5½ ft
3. Calculate l
l = 2w + 1 = 2 × 5½ + 1 = 11 + 1 = 12 ft
The rectangle is 12 ft long and 5½ ft wide.
