Question

A triangle has its base doubled and its

height increased by 30%. By what percent
has the area of the triangle increased?
(A) 130%
(B) 160%
(C) 230%
(D) 260%

Answer 1

Let the base and height of triangle be b and h.

area of triangle= 1/2*base*height

Area of triangle= bh/2

Now Base is Doubled and Height increase by 30%

New base = 2b

New height = h×130/100 = 13h/10

New area = 1/2 × 2b × 13h/10

New area = 13bh/10

Area increased = New area - area

Area increased = 13bh/10 - bh/2

Area increased= 13bh-5bh/10

Area increased= 8bh/10

Area increased= 4bh/5

ratio increased in % = Area increased/ Old Area × 100

ratio increased in % = 4bh/5 ÷ bh/2 × 100

ratio increased in % = 4/bh × 2/bh × 20

ratio increased in % = 8×20

ratio increased in % = 160%