Question
Let $\triangle ABC \sim \triangle DEF$ and their areas be respectively $81 cm^2$ and $144 cm^2$. If $EF =24 cm$, then length of side BC is....... cm .
✓
Answer
Let $\triangle\text{ABC}\sim\triangle\text{DEF}$ and their areas be respectively $81cm^2$ and $144cm^2$. If EF = 24cm, then length of side BC is 18cm.Solution:
$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\frac{\text{ar.}\triangle\text{ABC}}{\text{ar.}\triangle\text{DEF}}=\Big(\frac{\text{BC}}{\text{EF}}\Big)^2$
$\frac{81}{144}=\Big(\frac{\text{BC}}{24}\Big)^2$
$\frac{\text{BC}}{24}=\sqrt{\frac{81}{144}}$
$\frac{\text{BC}}{24}=\frac{9}{12}$
$\text{BC}=\frac{9}{12}\times24$
$\text{BC} = 18\text{cm}$
$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\frac{\text{ar.}\triangle\text{ABC}}{\text{ar.}\triangle\text{DEF}}=\Big(\frac{\text{BC}}{\text{EF}}\Big)^2$
$\frac{81}{144}=\Big(\frac{\text{BC}}{24}\Big)^2$
$\frac{\text{BC}}{24}=\sqrt{\frac{81}{144}}$
$\frac{\text{BC}}{24}=\frac{9}{12}$
$\text{BC}=\frac{9}{12}\times24$
$\text{BC} = 18\text{cm}$
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