Question

If each side of equilateral triangle becomes 4 times what is the percentage increase in in the area of the triangle

Answer 1

Step-by-step explanation:

let the side of equilateral triangle be a

area of equilateral triangle is √3/4 a^2

if side increased 4 times then the area will be

$\frac{ \sqrt{3} }{4} ( {4a)}^{2} \\ = \frac{ \sqrt{3} }{4} 16 {a}^{2} \\ = \sqrt{3} 4 {a}^{2}$

the percentage increase of area of equilateral triangle

$\frac{ \sqrt{3}4 {a}^{2} }{ \frac{ \sqrt{3} {a}^{2} }{4} } \times 100 \\ \frac{4}{ \frac{1}{4} } \times 100 \\ 4 \times 4 \times 100 \\ 16 \times 100 \\ 1600$

therefore the increase in area is 1600 %

hope you get your answer