Question

If the base of a triangle increase by 30 %and height reduce by 20%. Find the percentage change in area

Answer 1

Let the original base of the triangle be b

Let the original height of the triangle be h

Area of the original triangle = 1/2 * Base * Height

= 1/2 * b * h

= bh/2 sq.units = 0.5bh sq.units

Increased base of the new triangle = b + (b * 30/100)

= b + 3b/10

= {(10 * b) + 3b}/10

= (10b + 3b)/10

= 13b/10

Decreased height of the new triangle = h - (h * 20/100)

= h - 2h/10

= {(10 * h) - 2h}/10

= (10h - 2h)/10

=  8h/10

Area of the new triangle = Base * Height

= 13b/10 * 8h/10

= 26bh/25 sq.units = 1.04bh sq.units

Change in area = Area of the new triangle - Area of the original triangle

= 1.04bh - 0.5bh = 0.54bh sq.units

Change in percentage = Change in area/Area of the original triangle   *  100

= 0.54bh/0.5bh * 100

= 0.54/0.5 * 100

= 54/50 * 100

= 108%

Answer 2

Answer:

Let the area be 100 initially when b and h are not increased or decreased

1/2 * b * h = 100 ----- 1

base increased by 30% = 1.3 b( 1 + Percentage increase/100)

Hight reduced by 20% = 0.8 h (1- Percentage decrease/100)

New area is

1/2 * 1.3 b * 0.8 h = x ----- 2

Divide 1 and 2

1/1.04=100/x,  So x=104

INCREASE is 104-100/100 * 100 = 4%