Question

△ABC∼△DEF, △ABC has a height of 14 centimeters, and △DEF has a height of 6 centimeters. What is the ratio of the area of △ABC to the area of △DEF ?

Enter your answer, in simplest form.

Answer 1

14: 6 or 14 over 6.
divide by the GCF ( greatest common factor)
which is 2
14/2 = 7 6/2 = 3
The answer is 7:3

Answer 2

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

`\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}}=(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}} =(7)/(3)\\`

The ratio of the area of △ABC to the area of △DEF is 7:3