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If in a triangle angle ACB= …

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If in a triangle angle ACB= angle CDA,AC=6 and AD=3 then find the lenth AB

    • Posted by Ishika Bunkar 6 years, 1 month ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Apurva Vaidya 6 years, 1 month ago

    The length of AB is 12 cm. Step-by-step explanation: Given data: ∠ACB = ∠CDA AC = 6 cm AD = 3 cm To find: Length of AB From the figure attached below, in ∆ ABC & ∆ ACD, we have ∠A = ∠A ….. [∵ common angle for both the triangle] ∠ACB = ∠CDA ….. [∵ given] ∴ By AA similarity, ∆ABC ~ ∆ACD Since the sides of two similar triangles are proportional to each other ∴ \frac{AB}{AC} = \frac{AC}{AD} = \frac{BC}{CD} Now taking, \frac{AB}{AC} = \frac{AC}{AD} ⇒ AC² = AB * AD ⇒ 6² = AB * 3 …… [given AC = 6 cm & AD = 3 cm] ⇒ 36 = AB * 3 ⇒ AB = 36/3 = 12 cm

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