The sides of - ABC are 6 cm - 8 cm and 10 cm- Find the perimeter of the larger triangle which is similar to - ABC if the ratio of corresponding sides is 2 -A- 48 cmB- 24 cmC- 36 cmD- 12 cm

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Question

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

$48 c m$

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$36 c m$

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$24 c m$

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$12 c m$

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Solution

The correct option is A
$48 c m$

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 $X Z = 20 c m .$
The perimeter of $Δ XYZ$ is $X Y + Y Z + X Z = 12 + 16 + 20 = 48 c m .$

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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.

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

The correct option is A 48 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 perimeter of ΔXYZ is XY+YZ+XZ=12+16+20=48 cm.

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