The area of a triangle is 96. If the base of a triangle is tripled and the height is reduced to one-third its original length, what is the new area?
a) 3
b) 1/3
c) 9
d) The area would not change
The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height.
Let the original base and height of the triangle be b1 and h1, respectively. Then, we have:
A = (1/2)b1h1 = 96
If the base is tripled and the height is reduced to one-third, we get:
b2 = 3b1 and h2 = (1/3)h1
The new area, A2, is given by:
A2 = (1/2)b2h2 = (1/2)(3b1)(1/3)h1 = (1/2)b1h1 = A
Therefore, the new area is the same as the original area, and the answer is (d) The area would not change.