In traingle ABC, D and E are the points on sides AC and AB, respectively such that ∠ADE = ∠B. If AE = 8 cm, CD = 3 cm, DE = 6 cm and BC = 9 cm, then AD is equal to:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 9 cm
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Concept |
Understanding |
Application |
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If all three angles of 2 triangles are equal, then these two triangles are similar triangles. |
Given ∠ADE = ∠B AE = 8, CD = 3, DE = 6 and BC = 9 cm AD = ?
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In triangles ABC and ADE: Since ∠ADE = ∠B ∠A is common in both 3rd angle will also be equal Hence, triangles ABC and ADE are similar triangles. Hence, AE/AC = DE/BC ⇒ 8/AC = 6/9 ⇒ AC = 12 Now, AD = AC – CD = 12 – 3 = 9 cm |
