The sides of - ABC are 6 cm - 8 cm and 10 cm- Find the sides of the larger triangle which is similar to - ABC if the ratio of corresponding sides is2A- 3 cm - 4 cm and 5 cmB- None of theseC- 12 cm - 5 cm and 13 cmD- 12 cm - 16 cm and 20 cm

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Construction of a Similar Triangle - When Vertices Are Distinct

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Question

The sides of $Δ ABC$ are $6 c m, 8 c m$ and $10 c m .$ Find the sides of the larger triangle which is similar to $Δ ABC$ if the ratio of corresponding sides is 2.

$3 c m, 4 c m$ and $5 c m$

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$12 c m, 16 c m$ and $20 c m$

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$12 c m, 5 c m$ and $13 c m$

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None of these

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Solution

The correct option is B
$12 c m, 16 c m$ and $20 c m$

Let’s assume the triangle similar to $Δ ABC$ to be $Δ XYZ$ . The ratio of corresponding sides is 2.
So, $\frac{X Y}{A B} = \frac{Y Z}{B C} = \frac{X Z}{A C} = 2$ [Since, it is asked for larger triangle]
$\Rightarrow \frac{X Y}{6} = \frac{Y Z}{8} = \frac{X Z}{10} = 2$
$\Rightarrow X Y = 12 c m, Y Z = 16 c m$ and $X Z = 20 c m .$

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The sides of ΔABC are 6 cm, 8 cm and 10 cm. Find the sides of the larger triangle which is similar to ΔABC if the ratio of corresponding sides is 2.

The correct option is B 12 cm, 16 cm and 20 cm Let’s assume the triangle similar to ΔABC to be ΔXYZ. The ratio of corresponding sides is 2. So, XYAB=YZBC=XZAC=2 [Since, it is asked for larger triangle] ⇒XY6=YZ8=XZ10=2 ⇒XY=12 cm, YZ=16 cm and XZ=20 cm.

The sides of $Δ ABC$ are $6 c m, 8 c m$ and $10 c m .$ Find the sides of the larger triangle which is similar to $Δ ABC$ if the ratio of corresponding sides is 2.