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:  Therefore area decreases by  16 %.

Step-by-step

explanation:

Let height and base of the triangle be  x  and  y  units respectively.

40 % of  x=2x\5  

40 % of  y=2y\5  

Now since  x  is decreased and  y  is increased, let

x′=x−2x\5  

=3x\5  

y′=y+2y\5  

=7y\5  

Therefore the new height is  3x\5  and the new base is  7y\5 .

Let  A=xy\2  and  A′=3x\5×7x\52  

Dividing  A  by  A′ , we get  2521 . Let the areas be  25  unit  2  and  21  unit  2 .

Percent change  =100(final−initial)\intial  

Therefore percent change in area

=100(21−25)\25  

−16 %

Therefore area decreases by  16 %.

Answer 2

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

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