Question

If the sides of an equilateral triangle are increased by 20%, 30% and 50% respectively to form a new triangle, what is the percentage increase in the perimeter of the equilateral triangle?​

Answer 1

Answer:

$\huge{\mathcal{\underline{\green{AnSWer}}}}$

let each side of an equilateral triangle be $x$ cm

Then, after increase the three sides are

$(x + \frac{20}{100} x), \: \: (x + \frac{30}{100} x) , \: (x + \frac{50}{100} x) \\ </h2><p></p><h2>$

$i.e \: x + 0.2x, \: \: x + 0.3x, \: \: x + 0.5x </h2><p>\\ i.e \: \: 1.2x \: \: 1.3x \: \: 1.5x$

Original perimeter =3x

Increased perimeter=1.2x+1.3x+1.5x=4x

$\% \: Increase \: in \: perimeter$

$= \frac{increase \: in \: perimeter}{original \: perimeter} \times 100 \\ = ( \frac{4x - 3x}{3x} ) \times 100 \\ = \frac{x}{3x} \times 100 \\ = \frac{1}{3} \times 100 \\ = 33.33\%$