MCQ
$\triangle ABC \sim \triangle DEF$ such that $\operatorname{ar}(\triangle ABC )=64 cm^2$ and $\operatorname{ar}(\triangle DEF )=81 cm^2$. Then, the ratio of their corresponding sides is
- ✓$8: 9$
- B$36: 49$
- C$7: 9$
- D$9: 8$
✓
Answer
Correct option: A.
$8: 9$
$\because \triangle ABC \sim \triangle DEF$
$\therefore\left(\frac{AB}{DE}\right)^2=\frac{\operatorname{ar}(\triangle ABC)}{\operatorname{ar}(\triangle DEF)}=\frac{64}{81}$
$\frac{AB}{DE}=\sqrt{\frac{64}{81}}=\frac{8}{9}$
$\therefore$ the ratio of the corresponding sides is $8: 9$
$\therefore\left(\frac{AB}{DE}\right)^2=\frac{\operatorname{ar}(\triangle ABC)}{\operatorname{ar}(\triangle DEF)}=\frac{64}{81}$
$\frac{AB}{DE}=\sqrt{\frac{64}{81}}=\frac{8}{9}$
$\therefore$ the ratio of the corresponding sides is $8: 9$
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