Question No 48.In right ΔABC, where ∠C is the right angle, point D lies on side AB, and point E lies on side BC such that AC = CD, DE = EB, and the ratio AC : DE = 4 : 3. What is the ratio AD : DB?
Question
Question No 48.In right ΔABC, where ∠C is the right angle, point D lies on side AB, and point E lies on side BC such that AC = CD, DE = EB, and the ratio AC : DE = 4 : 3. What is the ratio AD : DB?
Solution
Given that AC = CD and DE = EB, we can infer that triangle ACD is congruent to triangle EDB by the Side-Angle-Side (SAS) congruence rule. This is because:
- AC = CD (Given)
- ∠ACD = ∠EDB (Both are right angles)
- AD = DE (Common side)
Since the two triangles are congruent, their corresponding sides are proportional. Therefore, the ratio AD : DB is equal to the ratio AC : CD, which is 4 : 3.
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