In ∆ABC, altitudes AD and BE are drawn. If AD = 7 cm, BE = 9 cm

Q) In ∆ ABC, altitudes AD and BE are drawn. If AD = 7 cm, BE = 9 cm and EC = 12 cm then, find the length of CD.

Ans:

Step 1: Let’s start with making a diagram for the question:

Step 2: Next, let’s compare Δ ADC and Δ BEC:

∠ ADC = ∠ BEC ( given AD and BE are altitudes hence both these angles are 90⁰)

∠ ACD = ∠ BCE (common angle)

Therefore, by AA similarity rule,

Δ ADC ~ Δ BEC

∴ $\frac{AD}{BE} = \frac{CD}{CE}$

by substituting the given values, we get:

$\frac{7}{9} = \frac{CD}{12}$

∴ CD = $\frac{7 \times 12}{9} = \frac{84}{9}$

∴ CD = 9.33 cm

Therefore, length of CD is 9.33 cm

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