Question

David made a triangle with sides 6 cm, 9cm and 12 cm. George wanted to make a triangle bigger in size but similar to that drawn by David. If the length of small side is 10 cm , find the length of other sides of the triangle drawn by David.​

Answer 1

Given :

$\triangle ABC \sim \triangle XYZ .$

$AB = 6\:cm, \:BC = 9 \:cm, CA = 12 \:cm$

$Let \: XY = 10\:cm, \:YZ = x \:cm, \: XZ = y /:cm$

$\frac{AB}{XY} = \frac{BC}{x} = \frac{CA}{y}$

$\blue {( The \: lengths \:of \: corresponding }$

$\blue {sides \:are \: proportional .)}$

$\implies \frac{6}{10} = \frac{9}{x} = \frac{12}{y}$

$i) \implies \frac{6}{10} = \frac{9}{x}$

$\implies x = \frac{9 \times 10}{6}$

$\implies x = 15\:cm$

$ii) \implies \frac{6}{10} = \frac{12}{y}$

$\implies y = \frac{12 \times 10}{6}$

$\implies y = 20\:cm$

Therefore.,

$\red { Value \:of \:x } \green { = 15\:cm }$

$\red { Value \:of \:y } \green { = 20\:cm }$

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