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jonny [76]
3 years ago
10

Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides? It would be a great he

lp

Mathematics
1 answer:
bija089 [108]3 years ago
4 0

Answer: AC= 10 cm and CE= 5 cm


Step-by-step explanation:

In the given picture, Δ ADE is a right triangle

∴ By Pythagoras theorem,

AD^2+DE^2=AE^2\\\Rightarrow\ (8+4)^2+9^2=AE^2\\\Rightarrow\ AE^2=12^2+9^2\\\Rightarrow\ AE^2=144+81=225\\\Rightarrow\ AE=15\ cm

Since triangles ABC and ADE are similar and corresponding sides of similar triangles are proportional therefore,

\frac{AB}{AC}=\frac{AD}{AE}\\\Rightarrow\frac{8}{AC}=\frac{12}{15}\\\Rightarrow\ AC=\frac{8\times15}{12}\\\Rightarrow\ AC=10\ cm

Now, AE=AC+CE

⇒CE=AE-AC

⇒CE=15-10=5 cm


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