Question

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

a) 3
b) 2 √3
c) 3 √3
d) 6

Answer 1

To find the length of AC in triangle ABC with the given conditions, we apply the Pythagorean theorem to the right triangle ADC, which yields AC as 2 √3 cm.

Step-by-step explanation:

In triangle ABC, with CD as an altitude and the given condition that AD equals BC, we aim to find the length of AC. Since AB equals 3 cm and CD equals √3 cm, we can apply the Pythagorean theorem because triangle ACD is a right triangle with CD as one leg and AD as the other leg, and AC as the hypotenuse. The relationship according to the Pythagorean theorem is given by:

a² + b² = c², where 'a' and 'b' are the legs of the right triangle and 'c' is the hypotenuse.

Let AD be 'a', CD be 'b', and AC be 'c'. We know 'b' is √3 cm. Since AD equals BC and AB equals 3 cm, AD must also be 3 cm. Plugging these values into the theorem, we get:

3² + (√3)² = c²

9 + 3 = c²

12 = c²

c = √12

c = 2 √3 cm. Thus, the length of AC is 2 √3 cm.