A 10-meter-long ladder reaches a window 8 meters above the ground. The distance from the base of the wall to the foot of the ladder is

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

The scenario forms a right-angled triangle with the ladder as the hypotenuse (10 m) and the wall as one side (8 m).
The Pythagorean theorem (a² + b² = c²) is used to find the length of the unknown side (the ground distance).
Substituting the values: 8² + b² = 10², which simplifies to 64 + b² = 100.
Solving for b gives b² = 36, so b = √36, which is 6 meters.

Option A: 4m is an incorrect calculation. It might result from a mistake in subtracting or finding the square root.
Option B: 5m is an incorrect calculation. This value does not satisfy the Pythagorean theorem with the given lengths.
Option D: 7m is an incorrect calculation. 8² + 7² = 64 + 49 = 113, which is not equal to 10² (100).

Visual 1: Diagram: A right-angled triangle labeled with 'Ladder (Hypotenuse) = 10m', 'Wall (Height) = 8m', and 'Ground (Base) = ?'. This helps visualize the relationship between the three elements and apply the Pythagorean theorem correctly.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Pythagorean Theorem as background academic context rather than a clinical decision trigger.
This question tests basic mathematical and logical reasoning skills, which are essential for nursing students.
Aptitude for quick calculation is necessary in clinical settings for tasks like drug dosage calculation, IV drip rate adjustment, and interpreting patient data.
What if the ladder was 12 meters long and the height was 8 meters? The calculation would change to 8² + b² = 12², leading to b² = 144 - 64 = 80, and b ≈ 8.94 meters. The principle remains the same.

How to Approach the Question

First, read the problem carefully and identify the geometric shape described. The ladder, wall, and ground form a right-angled triangle.
Identify the knowns and the unknown. The length of the ladder is the hypotenuse (c=10m), the height on the wall is one leg (a=8m), and the distance on the ground is the other leg (b=?).
Recall the relevant mathematical formula for a right-angled triangle, which is the Pythagorean theorem: a² + b² = c².
Substitute the known values into the formula: 8² + b² = 10².
Solve the equation for the unknown variable 'b'.
Compare your calculated result with the given options to find the correct answer.

Concept Tested & Keywords

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Practise the full ESIC Nursing Officer - 2019 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.