From a point P, Q is 5km due West and R is12km due South of Q. Find the distance between P and R.

1. Analyze the question

We are given the positions of three points: P, Q, and R.

• Q is 5km West of P.
• R is 12km South of Q.
• We need to find the straight-line distance between P and R.

2. Explain the concept

This problem involves bearings and directions, which can be visualized as a right-angled triangle.

• Moving "West" and "South" creates a 90-degree angle at point Q.
• Since we have a right-angled triangle where PQ and QR are the two legs, we can use the Pythagoras Theorem to find the hypotenuse (PR).
• Pythagoras Theorem: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse (the side opposite the right angle).

3. Show the solution

• Let $PQ = 5\text{ km}$ (base)
• Let $QR = 12\text{ km}$ (height)
• Let $PR = d$ (hypotenuse)

Using the formula: $PR^2 = PQ^2 + QR^2$ $PR^2 = 5^2 + 12^2$ $PR^2 = 25 + 144$ $PR^2 = 169$

To find $PR$, take the square root of both sides: $PR = \sqrt{169}$ $PR = 13\text{ km}$

4. Identify the answer

The distance between P and R is 13km. This corresponds to option C.

5. Tip

Whenever you see "North/South" combined with "East/West" in a geometry problem, immediately think of a right-angled triangle. Also, keep an eye out for Pythagorean Triples (like 3, 4, 5 or 5, 12, 13). Recognizing these triples can save you valuable time during your JAMB exam because you won't need to perform the full calculation!