Question

in the figure ABC similar to DEF area of triangle ABC 121 cmsquare and DEF is 64 cm square if the midean of triangle ABC is 12.1 find the midean of triangle DEF

Answer 1

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PLSS MRK BRAINLIEST

Answer 2

Answer:

Median of ∆DEF = 8.8 cm

Step-by-step explanation:

Given ∆ABC~∆DEF

and

Area of ∆ABC$A_{1}$ = 121 cm²

Area of ∆DEF=$A_{2}$= 64 cm²

Median of ∆ABC=$M_{1}$ = 12.1 cm

Median of ∆DEF=$M_{2}$

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By Theorem :

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians

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$\left(\frac{M_{2}}{M_{1}}\right)^{2}=\frac{A_{2}}{A_{1}}$

$\implies \left(\frac{M_{2}}{12.1}\right)^{2}=\frac{64}{121}$

$\implies \left(\frac{M_{2}}{12.1}\right)^{2}=\left(\frac{8}{11}\right)^{2}$

Now ,

$\implies \frac{M_{2}}{12.1}=\frac{8}{11}$

$\implies M_{2}= \frac{12.1\times 8 }{11}$

=$1.1\times 8$

=$8.8$

Therefore,

Median of ∆DEF = 8.8 cm

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