Step-by-step explanation:
Given :
\triangle ABC \sim \triangle XYZ .△ABC∼△XYZ.
AB = 6\:cm, \:BC = 9 \:cm, CA = 12 \:cmAB=6cm,BC=9cm,CA=12cm
Let \: XY = 10\:cm, \:YZ = x \:cm, \: XZ = y /:cmLetXY=10cm,YZ=xcm,XZ=y/:cm
\frac{AB}{XY} = \frac{BC}{x} = \frac{CA}{y}XYAB=xBC=yCA
\blue {( The \: lengths \:of \: corresponding }(Thelengthsofcorresponding
\blue {sides \:are \: proportional .)}sidesareproportional.)
\implies \frac{6}{10} = \frac{9}{x} = \frac{12}{y}⟹106=x9=y12
i) \implies \frac{6}{10} = \frac{9}{x}i)⟹106=x9
\implies x = \frac{9 \times 10}{6}⟹x=69×10
\implies x = 15\:cm⟹x=15cm
ii) \implies \frac{6}{10} = \frac{12}{y}ii)⟹106=y12
\implies y = \frac{12 \times 10}{6}⟹y=612×10
\implies y = 20\:cm⟹y=20cm
Therefore.,
\red { Value \:of \:x } \green { = 15\:cm }Valueofx=15cm
\red { Value \:of \:y } \green { = 20\:cm }Valueofy=20cm
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