If ΔABC ∼ Δ DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm2, then the area of the triangle DEF is :
Answer & explanation
Correct answer: option 4
Concept Used
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
⇒ \(\frac{Area\; of \; triangle\; ΔABC}{Area\; of \; triangle\; ΔDEF}\) = (\(\frac{BC}{EF}\))2
⇒ \(\frac{80}{Area\; of \; triangle\; ΔDEF}\) = (\(\frac{4}{5}\))2
⇒ \(\frac{80}{Area\; of \; triangle\; ΔDEF}\) = (\(\frac{16}{25}\))
⇒ Area of ΔDEF = \(\frac{80 \;×\; 25}{16}\) = 125 cm2
Therefore area of ΔDEF is 125 cm2.