Two similar triangles have area 490 sq. cm. and 640 sq. cm. If the length of the one side of the first triangle is 21 cm, then what is the length of the corresponding side of the second triangle?

Correct option is A

Given:
∆ABC ~ ∆DEF
​$$ar(ABC)=490 cm^2 \\\ \\ar(DEF)=640 cm^2$$​​
One side or AB =21cm
Formula Used:
​$$\frac{ar(ABC)}{ar(DEF)} = \frac{(AB)^2}{(DE)^2}= = \frac{(AC)^2}{(DF)^2}$$​​
Solution:
​$$\frac{ar(ABC)}{ar(DEF) }= \frac{(AB)^2}{(DE)^2 } \\\ \\\frac{(490)}{(640)}= \frac{21^2}{(DE)^2} \\\ \\\sqrt {\frac{ 49}{64}}=\frac{ 21}{DE}\\\ \\\frac{8}{7} \times 21 = DE \\\ \\24cm =DE$$​​