Delta XYZ sim Delta DEF for the correspondenc | vedclass

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Question

(C) Given that $\Delta XYZ \sim \Delta DEF$ with the correspondence $XYZ \leftrightarrow EDF$.This implies the ratio of corresponding sides is equal:

Vedclass · Accepted Answer

$39$

Vedclass · Answer

(C) Given that $\Delta XYZ \sim \Delta DEF$ with the correspondence $XYZ \leftrightarrow EDF$.This implies the ratio of corresponding sides is equal: $\frac{XY}{ED} = \frac{YZ}{DF} = \frac{ZX}{FE} = k$.Given $XY = 3, YZ = 4, ZX = 6$ and $DF = 12$.From the ratio $\frac{YZ}{DF} = \frac{4}{12} = \frac{1}{3}$,the scale factor $k = \frac{1}{3}$.Thus,$\frac{XY}{ED} = \frac{1}{3} \implies \frac{3}{ED} = \frac{1}{3} \implies ED = 9$.And $\frac{ZX}{FE} = \frac{1}{3} \implies \frac{6}{FE} = \frac{1}{3} \implies FE = 18$.The perimeter of $\Delta DEF = ED + DF + FE = 9 + 12 + 18 = 39$.

$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EDF$. If $XY = 3, YZ = 4, ZX = 6$ and $DF = 12$,find the perimeter of $\Delta DEF$.

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