Question

If $△ABC\sim △$ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of $△$ ABC and $△$ DEF.

• A. $\frac{25}{49}$
• B. $\frac{49}{16}$
• C. $\frac{36}{49}$
• D. $\frac{49}{9}$

Answer 1

The correct option is C

$\frac{36}{49}$

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides,

$\frac{areaof△ABC}{areaof△DEF}={\left(\frac{AB}{DE}\right)}^2={\left(\frac{12}{14}\right)}^2=\frac{36}{49}$