Solutions:
we are given that
△ABC∼△DEF
△ABC has a height of 14 centimeters, and △DEF has a height of 6 centimeters.
we have been asked to find the ratio of the area of △ABC to the area of △DEF ?
As we know , when two triangles are similar then their corresponding ratios are also equal.
So we can write
[tex] \frac{\text{Area of Triangle ABC }}{\text{Area of Triangle DE F }} =\frac{\text{Height of Triangle ABC }}{\text{Height of Triangle DE F}} \\\\\frac{\text{Area of Triangle ABC }}{\text{Area of Triangle DE F }} =\frac{\text{Height of Triangle ABC }}{\text{Height of Triangle DE F}}=\frac{14}{6} \\\\\frac{\text{Area of Triangle ABC }}{\text{Area of Triangle DE F }} =\frac{\text{Height of Triangle ABC }}{\text{Height of Triangle DE F}} =\frac{7}{3}\\ [/tex]
The ratio of the area of △ABC to the area of △DEF is 7:3
