△ADEF is similar to △AGHI. Length of DE is 16cm and length of the corresponding side GH is 25cm. What is the ratio of areas of △ADEF:△AGHI?
- A4:5
- B16:25
- C256 : 625
- D25 : 16
Solution & Step-by-step Explanation
For any two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Area(△AGHI)
Area(△ADEF)
=(
GH
DE
)
2
Given DE=16cm and GH=25cm:
Area(△AGHI)
Area(△ADEF)
=(
25
16
)
2
=
625
256
Therefore, the ratio of the areas is 256:625.
Area(△AGHI)
Area(△ADEF)
=(
GH
DE
)
2
Given DE=16cm and GH=25cm:
Area(△AGHI)
Area(△ADEF)
=(
25
16
)
2
=
625
256
Therefore, the ratio of the areas is 256:625.