Both triangle ABC and ADE in a figure are a right-angled isosceles triangle.
(length of BD) : (length of DC) = 1 : 3.
Find the area ratio of triangle DCE and triangle ABC.
(length of BD) : (length of DC) = 1 : 3.
Find the area ratio of triangle DCE and triangle ABC.
Answer
If it is set that CE = BD =1, since CE = BD, CE = 1.
Therefore, as for △ABC, length of base = BD + DC = 1 + 3 = 4, height is half of BC, it is 4 × 1/2 = 2 and the area is 4 × 2 / 2 = 4.
As for △DCE, lenght of base = DC = 3, height is CE = 1 and the area is 3 × 1 / 2 = 1.5.
3 : 8
Solution
As for △ABD and △ACE in a figure, AB = AC and AD = AE according to the conditions of the problem sentence.
Moreover, ∠BAD = ∠CAE = 90 degrees - ∠DAC.
Thus, △ABD and △ACE are congruent.
If it is set that CE = BD =1, since CE = BD, CE = 1.
Since ∠ACE = ∠ABD = 45 degrees and ∠ACB=45 degree, it turns out to be ∠ECD=90 degrees.
Therefore, as for △ABC, length of base = BD + DC = 1 + 3 = 4, height is half of BC, it is 4 × 1/2 = 2 and the area is 4 × 2 / 2 = 4.
As for △DCE, lenght of base = DC = 3, height is CE = 1 and the area is 3 × 1 / 2 = 1.5.
△DCE : △ABC = 1.5 : 4 = 3 : 8.
