The length of a rectangle is 5 times the width. The area is 720 square centimeters. Find the length and width of the rectangle.
Why did the rectangle go on a diet? Because it wanted to slim down its length-to-width ratio!
But no worries, let's solve the problem.
Let's call the width of the rectangle "x". According to the problem, the length is 5 times the width, so we can write the length as 5x.
The area of a rectangle is calculated by multiplying the length by the width:
Area = Length × Width
Since we already know that the area is 720 square centimeters, we can set up the equation:
720 = 5x × x
Now, let's solve for x:
720 = 5x^2
To simplify the equation, let's divide both sides by 5:
144 = x^2
Taking the square root of both sides, we find:
x = ±12
Since we're dealing with the length and width of a rectangle, we're gonna stick with the positive value. So, the width of the rectangle is 12 centimeters.
To find the length, we multiply the width by 5:
Length = 5 × Width
Length = 5 × 12
Length = 60 centimeters
So, the width of the rectangle is 12 centimeters and the length is 60 centimeters.
To find the length and width of the rectangle given the area, we can set up an equation using the formula for the area of a rectangle.
The formula for the area of a rectangle is:
Area = Length * Width
Given that the length of the rectangle is 5 times the width, we can represent the length as 5x and the width as x.
Substituting these values into the formula, we get:
720 = 5x * x
To solve this equation, we can rearrange it into quadratic form and then solve for x.
720 = 5x^2
Rearranging, we get:
5x^2 = 720
Dividing both sides of the equation by 5, we get:
x^2 = 144
Taking the square root of both sides of the equation, we get:
x = ±12
Since the width of a rectangle cannot be negative, we can discard the negative value.
Therefore, the width of the rectangle is 12 centimeters.
To find the length, we can substitute this value back into the equation for the length:
Length = 5 * width = 5 * 12 = 60 centimeters
Hence, the length of the rectangle is 60 centimeters and the width is 12 centimeters.