Question

The formula for the area of a triangle is A = bh/2.

If the base increases by 10%, and the height increases by 10%,
then the area A increases by X%. Find the exact value of X.

Answer 1

The formula for the area of a triangle is A = bh/2.

If the base increases by 10% from b to b(1+10/100) = b(1.1) and the height increases by 10% from h to h(1+10/100) = h(1.1)

then the new area A' = (b(1.1))(h(1.1))/2

To find the percentage increase in area we can use the formula:

X% = (A'-A)/A * 100%

Plugging in the values we have

X% = (b(1.1)h(1.1))/2 - bh/2 / bh/2 * 100%

Simplifying we get

X% = (bh(1.1)^2 - bh)/(bh/2) * 100% = (1.1)^2 * 100% - 100% = 21%

Therefore, the area A increases by 21%.

I hope this helps :)