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

3 cm, 4 cm and 5 cm

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12 cm, 16 cm and 20 cm

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12 cm, 5 cm and 13 cm

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None of these

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Solution

The correct option is B 12 cm, 16 cm and 20 cm
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 = 12 cm, YZ = 16 cm and XZ = 20 cm.

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