Question

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?

Answer 1

the area would have no change

Answer 2

The area of a triangle is given by:

$A = \frac{1}{2} * base * height$

Let us say initially base is "b" and height is "h" and area is 96

So Area is :

$96 = \frac{1}{2} * b * h$......................(1)

Now next we are given new base and height as:

Base is tripled,

B = 3b

Height is reduced to 1/3

H = h/3

So new area is :

$A = \frac{1}{2} * 3b * h/3$

So new Area becomes:

$A = \frac{1}{2} * b * h$..................(2)

Comparing (1) and (2), new and original area are same.

Answer : New area of triangle is same as original which is 96.