Triangles △ABC and △DEF are similar. Find the lengths of the sides of △DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.

Question

Sara Mccann

Mathematics

16 September, 18:29

Triangles △ABC and △DEF are similar. Find the lengths of the sides of △DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.

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Answers (1)

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Talia Mueller · Answer 1

DE = 1.5 cm, EF = 2.25 cm, FD = 3 cm

Step-by-step explanation:

Side DE corresponds to side AB and is (1.5 cm) / (2 cm) = 3/4 the length of it.

Because the triangles are similar, all pairs of corresponding sides have the same ratio. That is, the side lengths in ΔDEF are 3/4 of those in ΔABC.

... EF = (3/4) * BC = (3/4) * (3 cm)

... EF = 2.25 cm

... FD = (3/4) * CA = (3/4) * (4 cm)

... FD = 3 cm