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%?
See your 11-22-11, 2:36pm post for solution.
To find the percent change in the area of a triangle, we can use the formula:
Percent Change = (New Value - Old Value) / Old Value * 100%
In this case, the base is increased by 15% and the altitude is decreased by 25%. Let's assume the initial area of the triangle is A.
The new base would be 100% + 15% = 115% of the original base.
The new altitude would be 100% - 25% = 75% of the original altitude.
Therefore, the new area of the triangle would be (115% * 75%) of the original area, or 0.115 * 0.75 * A.
To find the percent change, we can substitute the new and old values into the formula:
Percent Change = (0.115 * 0.75 * A - A) / A * 100%
Simplifying the expression:
Percent Change = (0.08625 * A - A) / A * 100%
Percent Change = (-0.91375 * A) / A * 100%
Percent Change = -91.375%
Therefore, the area of the triangle will decrease by 91.375%.