The sides of - ABC have sides AB - BC - AC as 2 cm - 4 cm- and 6 cm respectively- Find the sides of the larger triangle which is similar to ABC- if the ratio of corresponding sides is 3 -A- 8 cm - 12 cm - 18 cmB- 6 cm - 12 cm - 18 cmC- 4 cm - 6 cm - 12 cmD- 5 cm - 7 cm - 9 cm

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The Mid-Point Theorem

The sides of ...

Question

The sides of $Δ ABC$ have sides AB, BC, AC as $2 c m, 4 c m, and 6 c m$ respectively. Find the sides of the larger triangle which is similar to $Δ ABC$ , if the ratio of corresponding sides is $3$ .

6 c m, 12 c m, 18 c m

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4 c m, 6 c m, 12 c m

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8 c m, 12 c m, 18 c m

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5 c m, 7 c m, 9 c m

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Solution

The correct option is A $6 c m, 12 c m, 18 c m$
Let’s assume the triangle similar to $Δ ABC$ to be $Δ XYZ$ . The ratio of corresponding sides is 3.

So, $\frac{X Y}{A B} = \frac{Y Z}{B C} = \frac{X Z}{A C} = 3$
$\Rightarrow \frac{X Y}{2} = \frac{Y Z}{4} = \frac{X Z}{6} = 3$
$∴ X Y = 6 c m$
$Y Z = 12 c m$
$X Z = 18 c m$

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The sides of ΔABC have sides AB, BC, AC as 2 cm,4 cm, and 6 cm respectively. Find the sides of the larger triangle which is similar to ΔABC, if the ratio of corresponding sides is 3.

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The sides of $Δ ABC$ have sides AB, BC, AC as $2 c m, 4 c m, and 6 c m$ respectively. Find the sides of the larger triangle which is similar to $Δ ABC$ , if the ratio of corresponding sides is $3$ .