Solution:
Given: • The perimeter of the rectangle Q = p
Working out: We need to find out the value of p
Statement 1: Each diagonal of the rectangle Q has length 10Let us assume that the length of the rectangle Q is l, and the breadth of the rectangle Q is b.
From this statement, we can infer that \(\sqrt{l^2 + b^2}\) = 10
• Squaring both the sides of the equation, we get \(l^2 + b^2 = 100\)
o There can be more than one possible combination of l and b.
o And hence, the sum of l and b is not unique.
Thus, Statement 1 alone is not sufficient to answer this question.
Statement 2: Area of the rectangle Q is 48 units. Let us assume that the length of the rectangle Q is l, and the breadth of the rectangle Q is b.
Thus, \(l*b = 48\)
There can be more than one combination of l and b: (6,8), (12, 4), etc. and the values of p will not be unique.
Thus, statement 2 alone is not sufficient to answer this question.
Combining both the statement: From statement 1, we have \(l^2 + b^2 = 100\)
From statement 2, we have \(l*b = 48\)
• \((l+b)^2 = l^2 + b^2 + 2l*b\)
• Or, \((l+b)^2 = 100 + 96\)
• Or, \((l+b)^2 = 196\)
• Or, \((l+b) = 14\) units.
From here, we can calculate the value of p.
Thus, combining both the statements, we got our answer.
Answer: Option C
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