a rectangle and a triangle have equal areas. the lenght of the rectangle is 12 inches ,and its width is 8 inches. if the base of the triangle is 32inches,what is the lenght,in inches of the altitude drawn to the base?
a)12
b)16
c)6
d)8
d)9
The area of the rectangle is 96 square inches.
The formula for finding the area of a triangle is A = 1/2bh
Solve for h.
would the answer be 12?
Let's see if 12 works.
96 = (32*12)/2
Nope that doesn't work, does it.
To find the length of the altitude drawn to the base of a triangle, we can use the formula for the area of a triangle:
Area of a triangle = (1/2) * base * height
In this case, we know that the area of the triangle is equal to the area of the rectangle. We can calculate the area of the rectangle using its length and width:
Area of a rectangle = length * width
Given that the length of the rectangle is 12 inches and the width is 8 inches, we can calculate its area as:
Area of rectangle = 12 * 8 = 96 square inches
Since the area of the triangle is equal to the area of the rectangle, we have:
Area of triangle = 96 square inches
Now, substituting the base of 32 inches into the area formula:
(1/2) * 32 * height = 96
Multiplying both sides by 2 to eliminate the fraction:
32 * height = 192
Dividing both sides by 32:
height = 6 inches
Therefore, the length of the altitude drawn to the base of the triangle is 6 inches (option c).