To find out how much the height of the triangle needs to decrease in order to keep the area constant when the base increases by 25%, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
1. Let's assume the original base is 100 units and the original height is 100 units. Therefore, the original area of the triangle is 1/2 * 100 * 100 = 5000 square units.
2. When the base increases by 25%, it becomes 125 units (100 + 25% of 100 = 125 units). To keep the area constant, we need to find the new height that corresponds to this new base.
3. Substituting the new base (125 units) and the original area (5000 square units) into the area formula, we get: 5000 = 1/2 * 125 * new height.
4. Solving for the new height, we get: new height = 5000 / (1/2 * 125) = 5000 / 62.5 = 80 units.
5. Therefore, the height needs to decrease from 100 units to 80 units, which is a decrease of 20 units.
6. To find the percentage decrease, we calculate: (20 / 100) * 100% = 20%.
Therefore, the correct answer is D) 20% – the height of the triangle needs to decrease by 20% to keep the area constant when the base increases by 25%.
