One side of a rectangle is 40 metres and its diagonal is 50 metres. Find the perimeter of this rectangle. & x… - RRB Staff Nurse Kolkata-2015

RRB Staff Nurse Kolkata-2015

Non Nursing Subjects

Hard

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The diagonal of a rectangle forms a right-angled triangle with two of its sides (length and width).
The Pythagorean theorem (a² + b² = c²) is used to find the length of the unknown side. Given one side as 40 m and the diagonal (hypotenuse) as 50 m, the other side is calculated to be 30 m.
The calculation is: 40² + b² = 50² → 1600 + b² = 2500 → b² = 900 → b = 30 m.
The perimeter of a rectangle is found using the formula P = 2 × (length + width).
Substituting the side lengths: P = 2 × (40 m + 30 m) = 2 × 70 m = 140 m.

Option A: This value is incorrect. It may result from a calculation error, such as incorrectly applying the perimeter formula, perhaps by adding the diagonal into the perimeter calculation in some way.
Option C: This value represents only the sum of the length and width (40 m + 30 m = 70 m). The formula for the perimeter requires this sum to be multiplied by 2.
Option D: This value is the sum of the given side and the diagonal (40 m + 50 m = 90 m). The diagonal is not part of the perimeter of a rectangle.

Visual 1: Diagram - A rectangle with its length labeled as 40 m, its width labeled as 30 m, and a dotted line representing the diagonal labeled as 50 m. This helps visualize the right-angled triangle within the rectangle.

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 rectangle using the Pythagorean theorem as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude and problem-solving skills, which are essential components of the non-nursing sections of nursing entrance examinations.
Strong foundational math skills are necessary for various nursing tasks, including medication dosage calculations, fluid balance monitoring, and interpreting graphical data from patient monitors.
What if the question gave the area and one side? If the area was 1200 m² and one side was 40 m, you would find the other side by dividing the area by the known side (1200 / 40 = 30 m), and then calculate the perimeter as 2 * (40 + 30) = 140 m.

How to Approach the Question

Step 1: Identify the given information in the problem: the length of one side of a rectangle (40 m) and the length of its diagonal (50 m).
Step 2: Recognize that the two sides of the rectangle and its diagonal form a right-angled triangle.
Step 3: Apply the Pythagorean theorem (a² + b² = c²) to find the length of the unknown side ('b'), where 'a' is the known side and 'c' is the diagonal.
Step 4: Solve the equation for the unknown side: b = √(c² - a²).
Step 5: Once you have the lengths of both sides, use the formula for the perimeter of a rectangle: P = 2 × (length + width).
Step 6: Calculate the final value and select the matching option.

Concept Tested & Keywords

Concept Tested: Calculating the perimeter of a rectangle using the Pythagorean theorem.
Stem keywords: rectangle, side, diagonal, perimeter
Lead-in keywords: Find

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