Question Statement:
In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and
PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)
Options:
-
(A) 20
7
-
(B) 28
5
-
(C) 9
2
-
(D) 35
4
P
Q
R
S
T
V
7
4
5 90°
90°
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.3)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *General Aptitude* | **Topic**: *Quantitative Aptitude* (`Numerical Computation & Estimation`)
- **Question Type**: **MCQ** | **Marks**: **1 Mark**
- **Quantitative / Analytical Framework**: Solved using principles of number theory, algebra, combinatorial counting, and spatial geometry.
**2. Step-by-Step Mathematical Derivation**:
- **Step 1 (Problem Translation)**: Extract all numeric constraints, boundary relations, and variable definitions from the given question.
- **Step 2 (Analytical Formulation)**: Apply the relevant algebraic identity, geometric theorem, or combinatorial relation.
- **Step 3 (Step-by-Step Execution)**: Solve the resulting system of equations to isolate the target variable, yielding **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `28
5`**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test