Question

In △ABC, CD is an altitude, such that AD = BC. Find AC, if AB = 3 cm, and CD = 3 cm.

Answer 1

Answer:

Let AD=BC=x; then BD = 3-x.

Step-by-step explanation:

Then in right triangle BDC the legs are 2 and 3-x and the hypotenuse is x. Use the Pythagorean Theorem to find the value of x.

Then in right triangle ABC the legs are AC and x and the hypotenuse is 3. Use the Pythagorean Theorem again to find the length of AC.

Answer 2

Answer:

Altitude has property that it falls at right angle.

So, we use pythagoras theorem it both ΔADC and ΔDBC.

In ΔADC

(AC)² = (AD)² + (DC)²

⇒ (AC)² = x² + 9

and in ΔDBC

(BC)² = (BD)² + (DC)²

⇒ x² = (3 - x)² + 9

Substituting this value of x in (AC)²

We get, (AC)² = (3 - x)² + 9 + 9

This is the method to solve this question.