Question

A man walks 8 km distance from a point S along a straight line to reach a point N. Then he turns 90 degrees and walks along a straight line to reach a point E. The distance between S and E is 17 km. Then the distance between N and E is:

• A. 15 km
• B. 17 km
• C. 12 km
• D. 16 km

Hint:

This problem uses the well-known Pythagorean triple \((8, 15, 17)\). Memorizing standard integer triples such as \((3,4,5)\), \((5,12,13)\), and \((8,15,17)\) allows you to spot missing right-triangle dimensions instantly without doing any scratchpad arithmetic.

Answer 1

The Correct Option is A

Concept: The directional movement described forms a geometric right-angled triangle. The turning point of \(90^{\circ}\) acts as the right-angled vertex. We apply the classical Pythagoras Theorem to resolve the lengths of the sides: \[ \text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2 \]

Step 1: Translating the spatial narrative into a geometric model.
Let the three structural coordinates be mapped as follows:
• Starting point is labeled as \(S\).
• First stopping point is labeled as \(N\). The distance segment \(SN = 8 \text{ km}\).
• The final destination is labeled as \(E\). The path forms a \(90^{\circ}\) angle at vertex \(N\), meaning \(\triangle SNE\) forms a right-angled triangle where the right angle is located at \(\angle SNE\).
• The direct straight line spatial displacement distance connecting \(S\) and \(E\) is given as \(SE = 17 \text{ km}\). This side lies opposite to the right angle, making it the hypotenuse.

Step 2: Formulating and evaluating using Pythagoras Theorem.
According to the theorem framework applied to \(\triangle SNE\): \[ SE^2 = SN^2 + NE^2 \] Substitute the known segment parameters into this relational equation: \[ 17^2 = 8^2 + NE^2 \] Let us evaluate the squares of these numbers: \[ 17^2 = 17 \times 17 = 289 \] \[ 8^2 = 8 \times 8 = 64 \] Now substitute these integer values back into the formula expression: \[ 289 = 64 + NE^2 \]

Step 3: Solving for the unknown distance segment \(NE\).
Isolate the variable term \(NE^2\) by subtracting 64 from both sides: \[ NE^2 = 289 - 64 \] \[ NE^2 = 225 \] Now, extract the square root of both sides to find the absolute linear value of \(NE\): \[ NE = \sqrt{225} = 15 \text{ km} \] Thus, the total path distance stretching from point \(N\) to point \(E\) is equal to \(15 \text{ km}\), matching Option (A).