Find the area of the square CDEF that is inscribed in the right triangle ABC as shown in the figure below.
Answer
Since ED = DC, AD : DC is also 1 : 2. 15cm of AC is distributed proportionally, it turns out to be that DC = 15cm × 2 / (1+2) = 10cm.
Therefore, the area of the square is 10 × 10 = 100 cm2.
100 cm2
Solution
△ABC and △AED are homothetic and homothetic ratio is AD : ED = 15 : 30 = 1 : 2.
Since ED = DC, AD : DC is also 1 : 2. 15cm of AC is distributed proportionally, it turns out to be that DC = 15cm × 2 / (1+2) = 10cm.
Therefore, the area of the square is 10 × 10 = 100 cm2.
