Question

In the given figure, in Δ ABC, AD ⊥ BC and ∠BAC = 90°. If BC = 16 cm and DC = 4 cm, then the value of x is ______.

Options

• 4 cm

• 5 cm

• 8 cm

• 3 cm

Answer 1

In the given figure, in Δ ABC, AD ⊥ BC and ∠BAC = 90°. If BC = 16 cm and DC = 4 cm, then the value of x is 8 cm.

Explanation:

Given

AD ⊥ BC

∠BAC = 90°

BC = 16cm

DC = 4cm

`"BD"/"AD" = "AD"/"DC"`    ...(∵ sides are proportional)

∴ AD² = BD × DC

AD² = 12 × 4

AD² = 48 cm

AD² + DC2 = AC

48 + 4² = x²

48 + 16 = x²

64 = x²

∴ x = 8 cm