Question

In Fig. 4.139,∠ABC= 90° and BD⊥AC. If BD = 8 cm and AD = 4 cm, find CD.

Answer 1

CD = 16 cm.

Step-by-step explanation:

In triangle Δ ABC, ∠ ABC = 90° and BD ⊥ AC.

Therefore, Δ ABC, Δ ABD, and Δ BCD all are right triangles.

From, Δ ABD, applying Pythagoras Theorem,

AB² = BD² + AD² = 8² + 4² ........... (1)

Again, from Δ BCD, applying Pythagoras Theorem,

BC² = BD² + CD² = 8² + x² ........... (2)

{Where, CD is assumed to be x cm}

Again, from big triangle Δ ABC, applying Pythagoras Theorem,

AC² = AB² + BC²

⇒ (AD + CD)² = AB² + BC²

⇒ (4 + x)² = 8² + 4² + 8² + x² {From equations (1) and (2)}

⇒ 4² + x² + 8x = 8² + 4² + 8² + x²

⇒ 8x = 2 × 8 × 8

⇒ x = 16 cm.

Therefore, CD = 16 cm. (Answer)