the length of a rectangle is 2 more than the width, the area of the rectangle is 15 ft. squared . find the length and width.
well since 15 = 3*5, I guess that pretty well solves the problem, no?
Width = W Ft.
Length = (W+2) Ft.
Area = (W+2)*W = 15Ft^2
W^2 + 2W - 15 = 0
C = -15 = -3*5
(W-3)(W+5) = 0
W-3 = 0
W = 3
W+5 = 0
W = -5. The width can't be negative.
Therefore, W = 3 Ft.
Length = W+2 = 3 + 2 = 5 Ft.
To find the length and width of the rectangle, we can use the information given about the relationship between the length and width, as well as the formula for the area of a rectangle.
Let's assign variables to the width and length. Let's say the width of the rectangle is 'w' feet. Since the length is 2 more than the width, we can say that the length is 'w + 2' feet.
The formula for the area of a rectangle is: Area = length * width.
Given that the area of the rectangle is 15 ft², we can set up the equation as follows:
15 = (w + 2) * w
Now we can solve this equation to find the value of 'w' (width).
Expanding the equation, we get:
15 = w^2 + 2w
Rearranging the equation in standard quadratic form:
w^2 + 2w - 15 = 0
Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's factor the equation:
(w + 5)(w - 3) = 0
Setting each factor to zero, we have:
w + 5 = 0 or w - 3 = 0
Solving these equations gives us two possible solutions for the width 'w':
w = -5 or w = 3
Since length and width cannot be negative, we discard the negative value. So, the width of the rectangle is 3 ft.
To find the length, we can substitute the value of 'w' back into the expression for length:
length = w + 2 = 3 + 2 = 5 ft
Therefore, the length of the rectangle is 5 ft and the width is 3 ft.