Question

The perimeter of the top of a rectangular table is 28 m, whereas its area is 48 m$^2$. What is the length of its diagonal?

• A. 5 m
• B. 10 m
• C. 12 m
• D. 12.5 m

Hint:

Use: - Sum = $l+b$ - Product = $lb$ Then apply Pythagoras for diagonal.

Answer 1

The Correct Option is B

Concept: For a rectangle:
• Perimeter $= 2(l + b)$
• Area $= l \times b$
• Diagonal $= \sqrt{l^2 + b^2}$

Step 1: Form equations.
\[ 2(l + b) = 28 \Rightarrow l + b = 14 \] \[ l \times b = 48 \]

Step 2: Solve for $l$ and $b$.
Two numbers whose sum is 14 and product is 48: \[ l = 8,\quad b = 6 \]

Step 3: Find diagonal.
\[ d = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \]

Step 4: Final conclusion.
Thus, the diagonal is: \[ 10 m \]