Question

A plate in the form of an equilateral triangle of side $l$ is cut into $16$ identical parts. The total edge length of all the smaller plates is?

• A. $3l$
• B. $9l$
• C. $12l$
• D. $16l$

Answer 1

The correct option is C $12l$

$P\alpha$ Side

$A\alpha (side{)}^2$

$\frac{A_1}{A_2}={\left(\frac{P_1}{P_2}\right)}^2$

$A_2=16A_1$

$\frac{1}{16}={\left(\frac{A}{P_2}\right)}^2$

$\frac{P_1}{P_2}=\frac{1}{4}$

$P_2=4P_1$

$=4\times 3l=12l$