Question

Based on the side lengths alone, could the triangles be similar?

Answer 1

Answer:

Yes, the sides are in the ratio 2:5.

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Answer 2

Answer:  The correct option is

(B) Yes, the sides are in the ratio 2:5.

Step-by-step explanation:  We are given to check whether the triangles can be similar based on the side lengths alone.

From the figure, we note that

the sides lengths of the triangle RST are

RS = 3.0 cm, ST = 6.0 cm  and RT = 6.4 cm.

and the corresponding side lengths of triangle XUW are

XU = 7.5 cm, UW = 15.0 cm  and  XW = 16.0 cm.

So, the ratio of the corresponding sides of the two triangles are as follows :

$\dfrac{RS}{XU}=\dfrac{3}{7.5}=\dfrac{30}{75}=\dfrac{2}{5},\\\\\\\dfrac{ST}{UW}=\dfrac{6}{15}=\dfrac{2}{5},\\\\\\\dfrac{RT}{XW}=\dfrac{6.4}{16}=\dfrac{64}{160}=\dfrac{2}{5}.$

Therefore, we get

$\dfrac{RS}{XU}=\dfrac{ST}{UW}=\dfrac{RT}{XW}=\dfrac{2}{5}=2:5.$

Hence, the corresponding sides are proportional and they are in the ratio 2 : 5.

Thus, (B) is the correct option.