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SOLUTION :
Given : ΔACB is right angled triangle at C = 90°.
From the figure : BC = 12 cm , AD=3 cm, DC = 2 cm.
AC = AD + DC = 3 +2= 5 cm
In ∆ACB,
AB² = AC² + BC² (by pythagoras theorem)
AB² = 5² + 12²
AB² = 25 + 144 = 169
AB= √169 = 13
AB = 13 cm
In ΔABC & ΔADE
∠BAC = ∠DAE (common)
∠ACB = ∠AED (each 90°)
ΔABC∼ΔADE (by A-A similarity criterion),
AB/AD = BC/DE = AC/AE
[Since corresponding sides of two similar triangles are proportional]
13/3 = 12/ DE = 5/AE
13/3 = 12/DE
13 DE = 12×3
DE = 36/13
13/3 = 5/AE
13 AE = 5×3
AE = 15/13
Hence, the length of DE= 36/13 & AE = 15/13
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