Final answer:
To increase the area of a triangle by 60% when its base is increased by 40%, the height should be increased by 33.33%.
Step-by-step explanation:
To find the percentage by which the height should be increased, we first need to understand the relationship between the base and height of a triangle and how it affects the area.
The area of a triangle is calculated using the formula: Area = 1/2 * base * height.
If the base of a triangle is increased by 40%, the new base will be 1.4 times the original base.
To maintain the same area, we need to increase the height of the triangle by a factor that compensates for the increase in the base.
Since the area needs to increase by 60%, the height should be increased by a factor of (60% / 40%) = 1.5
This means the height needs to be increased by 50%. Therefore, the correct answer is option b) 33.33%.