Question

In the given figure, DE║BC. If DE = 3cm, BC = 6cm and ar(ΔADE) = `15cm^2`, find the area of ΔABC.   

 

Answer 1

It is given that DE || BC
∴ ∠𝐴𝐷𝐸= ∠𝐴𝐵𝐶 (𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠)
∠𝐴𝐸𝐷= ∠𝐴𝐶𝐵 (𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠)
By AA similarity, we can conclude that Δ ADE ~ Δ ABC  

`(ar(ΔADE))/(ar(ΔABC))=(DE)^2/(BC)^2` 

⇒ `15/(ar(ΔABC))=3^2/6^2` 

⇒ `ar(ΔABC)=(15xx36)/9` 

= `60cm^2`
Hence, area of triangle ABC is `60 cm^2`