Question

A triangle is to be changed by increasing the length of its base by $40\%$ and decreasing the length of its height by $40\%$. What is the increase or decrease in the area of the triangle?

• A. It will increase by $40$%
• B. It will increase by $16$%
• C. It will not change
• D. It will decrease by $16$%

Answer 1

Answer: (D)

It will decrease by $16$%

If the original base is $b$ and the height is $h$,

then the original area of the triangle is $\frac{1}{2}\times b\times h=0.5bh$

If the triangle is to be changed by increasing the length of its base by $40\%$ and decreasing the length of its height by $40\%$,
then the new base will be $b+0.4b=1.4b$
and the new height will be $h-0.4h=0.6h$
So, the new area of triangle is $\frac{1}{2}\times 1.4b\times 0.6h$$=1.4\times 0.6\times 0.5bh$$=0.84\times 0.5bh$
As you see the new area is $0.84$ times the original area represents the new area is $84\%$ of the original area which means the area has decreased by $16\%$.
Hence, option $D$ is correct.