Answer:
150%
Step-by-step explanation:
The area is half base times height. We want the product to be the same, so if we scale one factor by f, we have to scale the other factor by 1/f to compensate.
Reducing by 60% is multiplication by f=1-60/100 = 0.4
So we have to multiply the height by 1/0.4=2.5 to compensate.
A factor of 2.5 is an increase of 150%
Check:
(1-60/100)(1+150/100) = 1, good
The height must be increased by 150% to keep the area of the triangle same.
A two-dimensional figure's area is the amount of space it takes up.
Area of triangle = (1 / 2)*B*H
B = Base of the triangle
H = Height of the triangle
Let the area of the triangle = A
Initially the base of the triangle = B
Initially the height of the triangle = H
A = (1 / 2)*B*H
H = (2A / B)
Area of the triangle = A
New base of the triangle = B₁ = B - (60/100)*B = (2 / 5)B
A = (1/2)*B₁*H₁
H₁ = (2A / B₁)
H₁ = 5A / B
New height of the triangle = H₁ = (5A / B)
Percentage increase in height = ((H₁ - H)/H) * 100
Percentage increase in height = ( (3A/B) / (2AB) ) * 100
Percentage increase in height = (3 / 2) * 100
Percentage increase in height = 150%
The height has to be increased by 150% to keep the area same.
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