The length of a rectangular banner is 3 feet longer than its width. If the area is 70 square feet, find the dimensions.
w(w+3) = 70
w^2 + 3w - 70 = 0
(w+10)(w-7) = 0
I guess that should help
17
Let's assume the width of the rectangular banner as "x" feet.
According to the given information, the length of the banner is 3 feet longer than its width, so the length can be expressed as "x + 3" feet.
The area of a rectangle is given by the formula: Area = length × width.
So, we can write the equation as:
x(x + 3) = 70
Expanding the equation:
x^2 + 3x = 70
Rearranging the equation to bring all terms on one side:
x^2 + 3x - 70 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula:
Factoring:
(x - 7)(x + 10) = 0
Setting each factor equal to zero:
x - 7 = 0 or x + 10 = 0
x = 7 or x = -10
Since the width cannot be negative, we disregard the x = -10 solution.
Therefore, the width of the rectangular banner is 7 feet.
And the length can be found by adding 3 to the width:
Length = 7 + 3 = 10 feet.
So, the dimensions of the rectangular banner are 7 feet by 10 feet.
To find the dimensions of the rectangular banner, we need to set up equations based on the information given.
Let's denote the width of the rectangular banner as "w" (in feet) and the length as "l" (in feet).
We are given two pieces of information:
1. The length is 3 feet longer than the width, which can be written as:
l = w + 3
2. The area of the rectangular banner is 70 square feet. The area of a rectangle is calculated by multiplying its length by its width, so we have:
Area = length * width
70 = l * w
Now we can substitute the value of "l" from equation 1 into equation 2:
70 = (w + 3) * w
Expanding the equation:
70 = w^2 + 3w
Rearranging the equation into a quadratic form:
w^2 + 3w - 70 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula.
Since -7 * 10 = -70 and -7 + 10 = 3, we can factorize the equation as follows:
(w + 10)(w - 7) = 0
Setting each factor to zero gives us two possibilities for the width:
w + 10 = 0 OR w - 7 = 0
Solving these two equations independently, we find:
w = -10 OR w = 7
We discard the negative value since the width cannot be negative, so the width of the rectangular banner is 7 feet.
Using equation 1, we can find the length:
l = w + 3
l = 7 + 3
l = 10
Therefore, the dimensions of the rectangular banner are 7 feet by 10 feet.