I don't understand this quadratic equation: The ratio of the measures of the length and width of a rectangle is 5:7. the area of the rectangle is 1,715 square feet. Find the dimensions of the rectangle.
length = 7 x
width = 5 x
7x * 5 x = 1715
35 x^2 = 1715
x^2 = 49
x = 7
7 x = 49
5 x = 35
To find the dimensions of the rectangle, we can use the information given about the ratio of the length to the width and the area of the rectangle.
Let's start by assigning variables to represent the length and width of the rectangle.
Let's say the length is 5x (since the ratio is 5:7) and the width is 7x.
The area of a rectangle is given by the formula: area = length x width.
In this case, the area is given as 1,715 square feet. So we can write the equation as:
(5x)(7x) = 1,715
Now, we can solve this quadratic equation to find the value of x.
Step 1: Simplify the equation by multiplying the coefficients:
35x^2 = 1,715
Step 2: Divide both sides of the equation by 35 to isolate the variable:
x^2 = 49
Step 3: Take the square root of both sides to solve for x:
x = ±√49
Since we're dealing with length and width dimensions, we can ignore the negative value. So, x = 7.
Now that we have the value of x, we can find the dimensions of the rectangle:
Length = 5x = 5(7) = 35 feet
Width = 7x = 7(7) = 49 feet.
Therefore, the dimensions of the rectangle are 35 feet by 49 feet.