If the height of a triangle is decreased by 40% and its base is increa

1.	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?1). No change2). 16% increase3). 8% decrease4). 16% decrease
Answer» We know that, AREA of a triangle = ½ × Base × Height Let us assume that the height and base of a given triangle are `H’ and `b’ respectively ∴ Area of the triangle = ½ × b × h----(1) Given that height of the triangle is decreased by 40% and base is INCREASED by 40% ⇒ NEW height of the triangle = h – (40h/100) = 3h/5 ⇒ New base of the triangle = b + (40b/100) = 7b/5 New area of the triangle = ½ × (3h/5) × (7b/5) = 21bh/50---(2) ∴ It is clear from (1) and (2) that Area of the new triangle is decreased Decrease in area = (bh/2) – (21bh/50) = 2bh/25 We know that, Percentage decrease in area = $(\frac{{{\rm{Decrease\ in\ area}}}}{{{\rm{Original\ area}}}} \TIMES 100)$ ∴ Percentage decrease in area = $(\frac{{\frac{{2bh}}{{25}}}}{{\frac{{bh}}{2}}} \times 100{\rm{}} = {\rm{}}16)$ ∴ The area of the triangle will be decreased by 16%

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?1). No change2). 16% increase3). 8% decrease4). 16% decrease

Answer»

We know that,

AREA of a triangle = ½ × Base × Height

Let us assume that the height and base of a given triangle are `H’ and `b’ respectively

∴ Area of the triangle = ½ × b × h----(1)

Given that height of the triangle is decreased by 40% and base is INCREASED by 40%

⇒ NEW height of the triangle = h – (40h/100) = 3h/5

⇒ New base of the triangle = b + (40b/100) = 7b/5

New area of the triangle = ½ × (3h/5) × (7b/5) = 21bh/50---(2)

∴ It is clear from (1) and (2) that Area of the new triangle is decreased

Decrease in area = (bh/2) – (21bh/50) = 2bh/25

We know that,

Percentage decrease in area = $(\frac{{{\rm{Decrease\ in\ area}}}}{{{\rm{Original\ area}}}} \TIMES 100)$

∴ Percentage decrease in area = $(\frac{{\frac{{2bh}}{{25}}}}{{\frac{{bh}}{2}}} \times 100{\rm{}} = {\rm{}}16)$

∴ The area of the triangle will be decreased by 16%