Triangle ABC ~ triangle DEF. The corresponding sides are in the ratio 3:4.
If area(DEF) - area(ABC) = $28 cm^{2}$ , find area(ABC) in $cm^{2}$ .

Question

Triangle ABC ~ triangle DEF. The corresponding sides are in the ratio 3:4. If area(DEF) - area(ABC) = 28 cm^2, find area(ABC) in cm^2.

Accepted Answer

36. Area ratio ABC:DEF = 9:16. Let parts = 9k and 16k. Difference 16k-9k = 7k = 28, so k = 4. Area(ABC) = 9 x 4 = 36 cm^2.

Step-by-Step Solution