The side of an equilateral triangle ABC is 28 cm. Find the side of another equilateral triangle PQR whose area is 16 times the area of triangle ABC.

Correct option is C

Given:
side of equilateral triangle ABC = 28cm
Formula Used:
Area of an equilateral triangle = $$\frac{√3}4$$​ × side²
Solution:
denote the side of triangle PQR as 'x'
the area of an equilateral triangle with side
the area of triangle ABC = $$\frac{√3}4 \times 28^2$$​​
area of triangle PQR is $$\frac{√3}4 \times x^2$$​​
the area of PQR is 16 times the area of ABC
​$$\frac{√3}4 \times x^2 = 16 \times \frac{√3}4 \times 28^2 \\ \ \\ x = 4 \times 28 \\ \ \\ x^2 = 16 \times 28^2$$​​
x = 112 cm
Alternate Method:
Two equilateral triangles are always similar.
​$$\frac{\text{Area of ΔABC}}{\text{Area of ΔPQR}} = \left(\frac{\text{Side of ABC}}{\text{Side of PQR}}\right)^2$$​​
=> $$\frac{1}{16} = \left(\frac{28}{x}\right)^2$$​​
=> $$\frac{28}x = \frac{1}{4}$$​​
=> x = 112 cm
Side of an equilateral triangle;
PQR = 112 cm