Question

In any \(\triangle ABC\), \(\angle A = 90^\circ\), BC = 13 cm, AB = 12 cm; then the value of AC is

• A. 3 cm
• B. 4 cm
• C. 5 cm
• D. 6 cm

Hint:

This is a classic example of a Pythagorean triple (5, 12, 13). If you recognize this triple, you can find the answer instantly without any calculation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The problem describes a right-angled triangle, since \(\angle A = 90^\circ\). We can use the Pythagorean theorem to find the length of the unknown side.

Step 2: Key Formula or Approach:
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
\[ (\text{Hypotenuse})^2 = (\text{Base})^2 + (\text{Perpendicular})^2 \] In \(\triangle ABC\) with \(\angle A = 90^\circ\), the hypotenuse is BC. So, \(BC^2 = AB^2 + AC^2\).

Step 3: Detailed Explanation:
We are given:
Hypotenuse, BC = 13 cm
One side, AB = 12 cm
We need to find the other side, AC.
Substitute the values into the theorem:
\[ 13^2 = 12^2 + AC^2 \] \[ 169 = 144 + AC^2 \] \[ AC^2 = 169 - 144 \] \[ AC^2 = 25 \] \[ AC = \sqrt{25} = 5 \] The length of AC is 5 cm.

Step 4: Final Answer:
The value of AC is 5 cm.