A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base?
32 h = 192
16 h = 96
h = 6
(triangle area) = (1/2)*32*h
= 96 (rectangle area)
32 h = 192
h = ? is the altitude you want
To find the length of the altitude drawn to the base of the triangle, we need to use the formula for the area of a triangle.
The area of a triangle can be calculated using the formula:
Area = (base * height) / 2
We know that the area of the rectangle is equal to the area of the triangle.
Area of rectangle = length * width = 12 * 8 = 96 square inches
So, the area of the triangle is also 96 square inches.
Using the formula, we can solve for the height (altitude) of the triangle:
96 = (32 * height) / 2
To find the height, we need to solve for it by isolating the variable:
96 * 2 = 32 * height
192 = 32 * height
Dividing both sides by 32, we get:
height = 192 / 32
height = 6 inches
Therefore, the length of the altitude drawn to the base of the triangle is 6 inches.
To find the length of the altitude drawn to the base of the triangle, we need to first calculate the area of both the rectangle and the triangle.
The area of a rectangle is given by the formula: length × width.
In this case, the length of the rectangle is 12 inches and the width is 8 inches. So, the area of the rectangle is 12 × 8 = 96 square inches.
Given that the area of the rectangle is equal to the area of the triangle, we can now proceed to find the area of the triangle.
The area of a triangle is given by the formula: (base × height) / 2.
In this case, the base of the triangle is given as 32 inches. To find the height, which is the altitude drawn to the base, we can use the formula: height = (2 × area) / base.
Since the area of the rectangle is 96 square inches, the area of the triangle is also 96 square inches. Substituting these values into the formula, we get:
height = (2 × 96) / 32 = 6 inches.
Therefore, the length of the altitude drawn to the base of the triangle is 6 inches.