Question

In the following figure, ∠ABC = 90° and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, find BD and AB.

Answer 1

Given:

∠ABC = 90°, BD ⟂ AC.

AD = 4 cm, CD = 5 cm. Hence AC = AD + CD = 4 + 5 = 9 cm.

Step-wise calculation:

1. Altitude-to-hypotenuse theorem (from similarity of the three right triangles) gives:

BD² = AD × CD

AB² = AD × AC

2. Compute BD:

BD² = AD × CD

= 4 × 5

= 20

BD = `sqrt(20)`

= `2sqrt(5)` cm (≈ 4.472 cm)

3. Compute AB:

AB² = AD × AC

= 4 × 9

= 36

AB = `sqrt(36)`

= 6 cm