△ABC ∼ △DEF such that ar(△ABC) = 64 cm2 and ar(△DEF)

Question:

△ABC ∼ △DEF such that ar(△ABC) = 64 cm2 and ar(△DEF) = 169 cm2 If BC = 4 cm, find EF

 

Solution:

We have △ABC ∼ △DEF
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

$\therefore \frac{\operatorname{area}(\triangle \mathrm{ABC})}{\operatorname{area}(\triangle \mathrm{DEF})}=\left(\frac{\mathrm{BC}}{\mathrm{EF}}\right)^{2}$

$\Rightarrow \frac{64}{169}=\left(\frac{\mathrm{BC}}{\mathrm{EF}}\right)^{2}$

$\Rightarrow\left(\frac{8}{13}\right)^{2}=\left(\frac{4}{\mathrm{EF}}\right)^{2}$

$\Rightarrow \frac{8}{13}=\frac{4}{\mathrm{EF}}$

$\Rightarrow \mathrm{EF}=6.5 \mathrm{~cm}$

 

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