Class CBSE Class 12 Mathematics Applications of Derivatives Q #701

Read the Passage

A technical company is designing a rectangular solar panel installation on a roof using 300 metres of boundary material. The design includes a partition running parallel to one of the sides dividing the area (roof) into two sections.

Let the length of the side perpendicular to the partition be $x$ metres and with parallel to the partition be $y$ metres.,
COMPETENCY BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) SUBJECTIVE
Write the equation for the total boundary material used in the boundary and parallel to the partition in terms of
x and y..
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Explanation
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Step-by-Step Solution

Let's analyze the given information:

  • The length of the side perpendicular to the partition is $x$ metres.
  • The length of the side parallel to the partition is $y$ metres.
  • There is a partition running parallel to one of the sides.
  • The total boundary material used is 300 metres.

The boundary consists of:

  • Two sides of length $x$
  • Two sides of length $y$
  • One partition of length $y$

Therefore, the total boundary material can be expressed as:

$2x + 2y + y = 300$

Simplifying the equation:

$2x + 3y = 300$

Correct Answer: 2x + 3y = 300

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their understanding of perimeter and geometric shapes to formulate an equation based on the given scenario.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of perimeter and how it relates to the dimensions of a rectangle, rather than recalling specific facts or performing a set procedure.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question is designed to assess the student's ability to apply mathematical concepts to a real-world scenario, aligning with competency-based education principles.

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