If the base of a triangle is shortened by 60 percent, by what percent must the height be increased if the area is to remain the same?

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