the length of a rectangle is twice its width, the area is 72sq inches,find its dimensions(find length and width)
by inspection, 6x12
a basketball team sells tickets that cost $10, $20, or vip seats, $30. the team has sold 492 tickets overall. it has sold 156 more $20 tickets than $10 tickets. the total sales are $8520. How many tickets of each kind have been sold?
To find the dimensions of the rectangle with the given information, we can set up an equation using the properties of rectangles.
Let's assume that the width of the rectangle is "w" inches. According to the problem, the length of the rectangle is twice its width, which means the length is "2w" inches.
The formula for the area of a rectangle is length × width. Given that the area is 72 square inches, we can set up the equation:
Area = Length × Width
72 = (2w) × w
Simplifying the equation further, we get:
72 = 2w^2
Now, we need to solve this quadratic equation to find the width of the rectangle.
1. Divide both sides of the equation by 2:
2w^2 = 72
w^2 = 36
2. Take the square root of both sides:
√w^2 = √36
w = ± 6
Since the width of a rectangle cannot be negative, we take the positive value:
w = 6 inches
Now that we have the width, we can find the length by substituting the value of the width back into the equation for length:
Length = 2w
Length = 2 × 6
Length = 12 inches
So, the dimensions of the rectangle are 12 inches (length) and 6 inches (width).