The area of a triangle is constant. Find the percentage increase in its perpendicular height if the base of the triangle is decreased by 20%.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 25% .
Let the base = b and height = h
Area of triangle = ½ × b × h (constant)
If base decreases by 20%, new base = 80% of b = 0.8b
Let new height = h₁
Since area is constant,
½ × b × h = ½ × 0.8b × h₁
h = 0.8h₁
h₁ = h / 0.8 = 1.25h
Increase in height = (1.25h − h) = 0.25h
Percentage increase = (0.25h / h) × 100 = 25%