The area of a triangle varies jointly as its base and altitude. By what percent will the area change if the base is increased by 15% and the altitude decreased by 25%?

(1.15)*(1.25) = 1.4375 is the change factor. Subtract 1 for the actal increase. Then convert that to %

There is a 43.75% increase

To find the percentage change in the area of a triangle when the base and altitude are changed, we need to understand how the area is related to the base and altitude.

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

According to the problem, the area varies jointly as the base and altitude. This means that the area is directly proportional to the product of the base and altitude.

Mathematically, we can express this relationship as:
Area = k * base * altitude

where "k" is the constant of variation.

Now, let's analyze the given scenario. The base is increased by 15%. This means the new base is 100% + 15% = 115% of the original base. Similarly, the altitude is decreased by 25%. This means the new altitude is 100% - 25% = 75% of the original altitude.

To find the percentage change in the area, we can compare the new area to the original area.

Original Area = k * base * altitude
New Area = k * (1.15 * base) * (0.75 * altitude)
= (1.15 * 0.75) * k * base * altitude

Let's denote the original area as A1 and the new area as A2.

A1 = k * base * altitude
A2 = (1.15 * 0.75) * k * base * altitude

Now, we can calculate the percentage change in the area using the following formula:

Percentage Change = (|A2 - A1| / A1) * 100

Let's substitute the values:

Percentage Change = (|A2 - A1| / A1) * 100
= (|1.15 * 0.75 * k * base * altitude - k * base * altitude| / (k * base * altitude)) * 100
= [(1.15 * 0.75 - 1) * 100] percent

Calculating the value inside the brackets:

(1.15 * 0.75 - 1) * 100 = (0.8625 - 1) * 100
= -0.1375 * 100
= -13.75 percent

Therefore, the area of the triangle will decrease by 13.75%.