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 is 2 -A- 3 cm - 4 cm and 5 cmB- 12 cm - 16 cm and 20 cmC- 12 cm - 5 cm and 13 cmD- None of these

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Question

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

3cm, 4cm and 5cm

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12cm, 16cm and 20cm

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12cm, 5cm and 13cm

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None of these

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Solution

The correct option is B 12cm, 16cm and 20cm
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)
$\Rightarrow \frac{X Y}{6} = \frac{Y Z}{8} = \frac{X Z}{10} = 2$
$\Rightarrow$ XY = 12cm, YZ = 16cm and XZ = 20 cm.

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The sides of ΔABC are 6cm, 8cm and 10cm. 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 12cm, 16cm and 20cmLet’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 = 12cm, YZ = 16cm and XZ = 20 cm.

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