Question

If the height of a triangle is decreased by 40% and it's base is increased by 40%, what will be the effect on its area ?​

Answer 1

Answer:

$\huge\underline\bold {Question:}$

If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area ?

$\huge\underline\bold {Answer:}$

Let the original base and height of the triangle be b units and h units respectively. Then,

Original area

$= \frac{1}{2} bh = 0.5bh$

New base

$= b + 40\% \: \: of \: \: b \: \: = 1.4b$

New height

$= h - 40\% \: \: of \: \: h \: = 0.6h$

Therefore, new area

$= \frac{1}{2} \times 1.4b \times 0.6h = \frac{0.84bh}{2} \\ = 0.42bh$

Decrease in area

$= 0.5bh - 0.42bh = 0.08bh$

Therefore per cent decrease

$= \frac{0.08bh}{0.5bh} \times 100 \\ = 16\%$