The length of the diagonal of a square is 25 cm, then the perimeter of this square is:

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

Explanation

The relationship between a square's diagonal (d) and its side (a) is given by the formula d = a√2, derived from the Pythagorean theorem.
Given the diagonal d = 25 cm, we can solve for the side: a = d/√2 = 25/√2 cm.
The perimeter (P) of a square is calculated using the formula P = 4a.
Substituting the value of 'a', we get P = 4 × (25/√2) = 100/√2 cm.
Rationalizing the denominator gives P = (100√2)/2, which simplifies to 50√2 cm.

Option A: This value is obtained by incorrectly assuming the side length is equal to the diagonal length and calculating the perimeter as 4 × 25 = 100 cm.
Option C: This result likely stems from a calculation error, possibly by incorrectly multiplying by √2 instead of dividing when finding the side length from the diagonal.
Option D: This value represents the diagonal of a square with a side length of 25 cm (d = a√2), not the perimeter.

Visual 1: Diagram: A square with its sides labeled 'a' and its diagonal labeled 'd = 25 cm'. This helps visualize the right-angled triangle formed by two sides and the diagonal, which is the basis for the formula d = a√2.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the perimeter of a square from its diagonal as background academic context rather than a clinical decision trigger.
This is a general aptitude and reasoning question, designed to test mathematical and problem-solving skills which are essential for nurses.
While not a direct clinical calculation, the logical reasoning and precision required are similar to skills needed for tasks like medication dosage calculations and interpreting quantitative data from patient monitoring equipment.
What if the question asked for the area? You would first find the side 'a' (25/√2 cm) and then square it: Area = a² = (25/√2)² = 625/2 = 312.5 cm².

How to Approach the Question

First, identify the given information: the shape is a square and its diagonal (d) is 25 cm.
Next, identify what you need to find: the perimeter (P) of the square.
Recall the relationship between a square's diagonal and its side (a): d = a√2.
Use this formula to calculate the length of one side (a) from the given diagonal.
Once you have the side length, use the formula for the perimeter of a square: P = 4a.
Perform the calculation and simplify the result, ensuring to rationalize the denominator if necessary. Compare your final answer with the given options.

Concept Tested & Keywords

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