A rectangle is 7 feet longer than it is wide. If its area is 120 square feet, find its length and width. Represent this situation as an equation and solve.
L=7+w
A=LW
120=(7+w)w
120=7w+w^2
w^2+7w-120=0
(w+15)(w-8)=0
w=-15 or w=8. Length cannot be negative.
Width is 8 ft. Length is 15 ft.
A rectangle has an area of 120 square feet and a width of 8 feet what is the length of the rectangle
Let's represent the width of the rectangle as "w".
According to the given information, the length of the rectangle is 7 feet longer than the width. So, the length can be represented as "w + 7".
The formula to calculate the area of a rectangle is: Area = Length * Width.
We are given that the area is 120 square feet. Therefore, we can set up the equation:
Area = Length * Width
120 = (w + 7) * w
Now, let's solve this equation step-by-step:
Step 1: Distribute the w to the terms on the right side:
120 = w^2 + 7w
Step 2: Move all the terms to one side to set up the equation in standard form:
w^2 + 7w - 120 = 0
Step 3: Factorize the quadratic equation:
(w - 8)(w + 15) = 0
Step 4: Set each factor equal to zero and solve for w:
w - 8 = 0 --> w = 8
w + 15 = 0 --> w = -15
Since width cannot be negative, we ignore the solution w = -15.
Therefore, the width of the rectangle is 8 feet.
To find the length, substitute the width value (w = 8) into the equation for length:
Length = Width + 7
Length = 8 + 7
Length = 15
So, the length of the rectangle is 15 feet and the width is 8 feet.
To solve this problem, we can start by representing the width of the rectangle as "x" (in feet).
According to the given information, the length of the rectangle is 7 feet longer than the width. So, the length can be represented as "x + 7" (in feet).
The area of a rectangle can be calculated by multiplying its length and width. In this case, the area is given as 120 square feet.
Using the formula for the area of a rectangle, we have:
Length × Width = Area
(x + 7) × x = 120
Now, we can solve the equation to find the values of x (width) and x + 7 (length).
Expanding the equation, we get:
x^2 + 7x = 120
Rearranging the equation to standard quadratic form, we have:
x^2 + 7x - 120 = 0
To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. In this case, let's factor it:
(x + 15)(x - 8) = 0
Setting each factor equal to zero, we get:
x + 15 = 0 or x - 8 = 0
Solving for x, we have two possible solutions:
x = -15 (not a valid width since it can't be negative) or x = 8.
Since the width cannot be negative, we discard x = -15 as a solution.
Therefore, the width of the rectangle is x = 8 feet.
To find the length, we can substitute this value back into the expression for length:
Length = x + 7 = 8 + 7 = 15 feet.
Hence, the width of the rectangle is 8 feet and the length is 15 feet.