The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?

Appeared in: HSSC Staff Nurse - 2015

Explanation

The perimeter of a rectangle is given by the formula P = 2(L + B), where L is length and B is breadth.
Given the perimeter is 206 m, we can form the equation 2(L + B) = 206, which simplifies to L + B = 103.
We are also given that the difference between length and breadth is 23 m, so L - B = 23.
Solving these two linear equations simultaneously gives L = 63 m and B = 40 m.
The area of the rectangle is calculated as Length × Breadth, which is 63 m × 40 m = 2520 m².

Option A: This value is a result of incorrect calculation, likely an error in either solving for the dimensions or in the final multiplication.
Option B: This value is a result of incorrect calculation. It does not correspond to the product of the correctly derived length and breadth.
Option C: This value is a result of incorrect calculation. For example, multiplying 62 by 40 gives 2480, which might arise from a simple subtraction error when finding the breadth.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the area of a rectangle using its perimeter and the difference between its sides as background academic context rather than a clinical decision trigger.
This question tests fundamental mathematical skills in geometry and algebra, which are often part of the general aptitude section in nursing and other competitive entrance exams.
The ability to translate a word problem into a system of mathematical equations is a critical thinking skill assessed in these exams.
What if the sum of length and breadth was given instead of the perimeter? If the sum (L+B) was 103m, the first step of dividing the perimeter by 2 would be skipped, and you would directly use the sum equation with the difference equation to solve for L and B.

How to Approach the Question

First, carefully read the question and identify the given information: the perimeter of the rectangle (206 m) and the difference between its length and breadth (23 m).
Recall the formula for the perimeter of a rectangle: P = 2(L + B).
Set up the first equation using the given perimeter: 2(L + B) = 206. Simplify this to L + B = 103.
Set up the second equation using the given difference: L - B = 23.
You now have a system of two linear equations. Solve them simultaneously. A quick method is to add the two equations together to eliminate B and solve for L.
Once you have the value for L, substitute it back into either equation to find the value of B.

Concept Tested & Keywords

Concept Tested: Calculating the area of a rectangle using its perimeter and the difference between its sides.
Stem keywords: rectangle, length, breadth, perimeter, area, difference
Lead-in keywords: then its area is?

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