The width of a rectangle is 2ft less than its length. The area is 8ft^2. Find the length and width.
I can't seem to come up with anything that equals 64 sq ft.
Do I start with area 64sqft.=W x L-2.
I feel like I should be coming up with something around 7 times 9 but I can't seem to come up with 64, ideas?
In the first statement you say area is 8 ft^2
Then you say it is 64 ft^2
If it is eight, it is obvious by inspection
2*4 = 8
If it is 64, we better try to do it right
W * (W+2) = 64
W^2 + 2 W - 64 = 0
W = -2/2 +/- (1/2)sqrt (4 + 4*64)
W = -1 +/- (1/2) sqrt ( 4*65)
W = -1 +/- sqrt(65)
W = -1 - sqrt 65 forget this solution, no negative width
W = 8.06 - 1 = 7.06
W + 2 = 9.06
so indeed very close to 7 and 9
x(x+2) = 64
If you are studying quadratic equations, you should be able to solve this one.
It comes out as a radical
(7.0622 and 9.0622)
You are right. I should sleep and try again later. I am starting to make silly mistakes.
To solve this problem, you first need to set up an equation based on the given information. Let's start by assuming the length of the rectangle is x ft. According to the problem, the width is 2 ft less than the length, which means the width is x - 2 ft.
The formula for the area of a rectangle is length multiplied by width, so the area equation can be written as:
Area = Length × Width
8 ft² = x ft × (x - 2) ft
Now, we can solve this quadratic equation to find the value of x (length). To do so, we need to expand and rearrange the equation:
8 ft² = x² - 2x
0 = x² - 2x - 8 ft²
To factorize the equation, we need to find two numbers that multiply to give -8 (the coefficient of x²) and add up to -2 (the coefficient of x).
The factors of -8 are:
-8 and 1
-4 and 2
4 and -2
8 and -1
Out of these pairs, the numbers that add up to -2 are -4 and 2. So, we can rewrite the equation as:
0 = (x - 4)(x + 2)
Using the zero product property, we can solve for x by setting each factor equal to zero:
x - 4 = 0 or x + 2 = 0
Solving these equations gives us:
x = 4 or x = -2
Since the length cannot be negative, we discard the solution x = -2. Therefore, the length of the rectangle is x = 4 ft.
To find the width, we substitute the length value back into the width equation:
Width = Length - 2
Width = 4 ft - 2 ft
Width = 2 ft
So, the length of the rectangle is 4 ft, and the width is 2 ft.