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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

Triangles A...

Question

Triangles $A B C$ and $D E F$ are similar .The area of $△ A B C$ is $16 c m^{2}$ , and that of $△ D E F 25 c m^{2}$ . If $B C = 2.3 c m$ , find $E F$ .

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Solution

$Δ A B C \sim Δ D E$

$Δ A B C = 16 c m^{2}$

$Δ D E F = 25 c m^{2}$

$B C = 2.3 c m$

$E F = ?$

Ratio of area is equal to square of ratios of its corresponding sides

Hence, $\frac{Δ A B C}{Δ D E F} = {(\frac{B C}{E F})}^{2}$

$\frac{16}{25} = \frac{2.3 \times 2.3}{E F^{2}}$

$E F = \sqrt{8.265625}$

$∴ E F = 2.875 c m$

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