Question

The base of a triangle is increased in length by 20% and its height reduced by 20%. How does its area change?

• A. reduced by 4%
• B. increased by 4%
• C. does not change
• D. reduced by 4.166%
• E. increases by 4.166 %

Answer 1

The Correct Option is A

The correct answer is option (A):

reduced by 4%

Let's break down how the area of a triangle changes when its base and height are altered.

The formula for the area of a triangle is: Area = (1/2) * base * height

Let's say the original base is 'b' and the original height is 'h'. The original area is then (1/2) * b * h.

Now, the base is increased by 20%. This means the new base is b + 0.20b = 1.20b.

The height is reduced by 20%. This means the new height is h - 0.20h = 0.80h.

The new area is (1/2) * (1.20b) * (0.80h) = 0.96 * (1/2) * b * h

Notice that the new area is 0.96 times the original area. This represents a change:

* The area has been multiplied by 0.96.
* The original area is considered 1. So the change is 1-0.96 = 0.04.
* This represents a reduction of 0.04 which is the same as a 4% decrease.

Therefore, the area is reduced by 4%.