Evan is making a table that will be created in the shape of the figure below. The table top is a triangle attached to a rectangle. To purchase the right amount of paint, he needs to know the area of the table top. He can only spend $10 on paint, which is enough to cover 150 ft2 of surface area. What is the maximum length of the base of the rectangle he can build?
An image of a compound shape made up of a rectangle and a triangle is shown. The length of the rectangle is labeled x and the width is labeled 6 feet. The base of the triangle is labeled 4 feet and the height is labeled 6 feet.
well, the triangle obviously has area = 12
So, the whole outfit has area 6x+12. So,
6x+12 = 150
6x = 138
x = 23
To find the maximum length of the base of the rectangle, we need to calculate the area of the table top.
The area of the rectangle is given by the formula: Area = length x width
The area of the triangle is given by the formula: Area = (base x height) / 2
Let's calculate the area of the table top by adding the areas of the rectangle and triangle.
Area of the rectangle = x * 6
Area of the triangle = (4 * 6) / 2
Total area = Area of the rectangle + Area of the triangle
Since he can only spend $10 on paint, which is enough to cover 150 ft^2 of surface area, we can set up the following equation:
Total area = 150 ft^2
Substituting the values we calculated:
150 ft^2 = (x * 6) + (4 * 6) / 2
Now, we can solve for x:
150 ft^2 = 6x + 12 ft^2
Subtracting 12 ft^2 from both sides:
138 ft^2 = 6x
Dividing both sides by 6:
23 ft^2 = x
Therefore, the maximum length of the base of the rectangle Evan can build is 23 feet.
To find the maximum length of the base of the rectangle, we need to calculate the area of the table top.
The table top consists of a rectangle and a triangle. We can calculate the area of the rectangle by multiplying its length (x) by its width (6 feet). The area of the rectangle is then 6x square feet.
The area of the triangle can be found by multiplying half of the base (4 feet) by the height (6 feet). The area of the triangle is 12 square feet.
To find the total area of the table top, we can add the area of the rectangle and the area of the triangle together: Area = (6x + 12) square feet.
We know that Evan can only spend $10 on paint, which is enough to cover 150 square feet of surface area. Therefore, we can set up the following equation:
(6x + 12) = 150
Now we can solve this equation to find the maximum length of the base of the rectangle.
First, subtract 12 from both sides of the equation:
6x = 138
Next, divide both sides of the equation by 6:
x = 23
Therefore, the maximum length of the base of the rectangle that Evan can build is 23 feet.