Question

triangle ABC similar to triangle ADE . If AE = 2 cm , EC = 3 cm DE = 1.6 cm then find BC

Answer 1

We have triangle ABC and triangle ADE,

AE/AC=ED/BC (Thales or bpt theorem)

Here, AC=AE+EC=2+3=5

2/1.6=5x

x=1.6*5/2=4

Hence, BC=4

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Answer 2

Answer:

The length of line segment BC = 4 cm

Step-by-step explanation:

Given that : ΔABC ~ ΔADE

Now, The sides of the two similar triangles are proportional to each other

$\implies\frac{BC}{DE}=\frac{AC}{AE}\\\\\implies\frac{BC}{DE}=\frac{AE+EC}{AE}\\\\ \implies BC=\frac{(AE+EC)\times DE}{AE}\\\\\implies BC=\frac{(2+3)\times 1.6}{2}\\\\ \implies BC=\frac{5\times 1.6}{2}\\\\\implies BC=5\times 0.8\\\\\bf\implies BC=4\:\:cm$

Thus, The length of line segment BC = 4 cm