Question

In the following figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find AC.

Answer 1

Given:

∠ABC = 90°, BD ⟂ AC (so BD is the altitude to hypotenuse AC).

AB = 5.7 cm, BD = 3.8 cm, CD = 5.4 cm. (We denote AD = AC – CD.)

Step-wise calculation:

1. Use the altitude relation:

BD² = AD × CD

BD² = 3.8² = 14.44

So `AD = (BD^2)/(CD)` 

= `14.44/5.4` 

= 2.674074074... cm

2. Then AC = AD + CD

= 2.674074074... + 5.4

= 8.074074074... cm

3. Rounding to two decimal places:

AC ≈ 8.07 cm