Question

in triangle abc angle b is equals to 90 degrees and BD perpendicular to AC .DC =7cm. AD= 3 cm then find the length of BD

Answer 1

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Answer 2

Answer:

The length of BD is $\sqrt{21}cm$

Step-by-step explanation:

Given in triangle abc angle b is equals to 90° and BD perpendicular to AC. DC =7cm. AD= 3 cm. we have to find the value of BD.

Let ∠BAD=Ф ⇒ ∠BCD=90-Ф  (As ∠B=90° and ∠A+∠B+∠C=180°)

Also if ∠BAD=Ф ⇒ ∠ABD=90-Ф

If ∠BCD=90-Ф ⇒ ∠DBC=Ф

In ΔABD and ΔBDC

∠BAD=∠DBC=Ф        (Proved above)

∠ABD=∠BCD             (Proved above)

By AA similarity rule, ΔABD~ΔBDC

hence, we can write

$\frac{AD}{BD}=\frac{BD}{CD}\\\\\frac{3}{BD}=\frac{BD}{7}\\\\BD^2=21\\\\BD=\sqrt{21}cm$