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The area of a triangle is 124 square units. What would its new area be if its base was half as long, and its height was three times as long?
(2 points)
First, we need to remember the formula for the area of a triangle, which is A = 1/2 * base * height.
Given that the original area is 124 square units, we can write:
124 = 1/2 * base * height
Now we are asked to find the new area when the base is half as long and the height is three times as long. Let's represent the new base as b' and the new height as h'.
We have the following equations:
b' = 1/2 * base
h' = 3 * height
We know that the new area A' will be equal to 1/2 * b' * h', so:
A' = 1/2 * (1/2 * base) * (3 * height)
Substitute the given area equation into the equation for A':
A' = 1/2 * (1/2 * 124) * (3)
A' = 1/2 * 62 * 3
A' = 31 * 3
A' = 93
Therefore, the new area of the triangle would be 93 square units.