Question : The perimeter of a rectangle is 30 cm. If the length of the rectangle is twice its breadth, then what is the length of its diagonal?
Option 1: $5 \sqrt{5}\text{ cm}$
Option 2: $3 \sqrt{2} \text{ cm}$
Option 3: $4 \sqrt{5} \text{ cm}$
Option 4: $5 \sqrt{4} \text{ cm}$
Correct Answer: $5 \sqrt{5}\text{ cm}$
Solution :
Perimeter of a rectangle = 2 × (l + b)
Diagonal = $\sqrt{l^2 + b^{2}}$, where $l$ and $b$ are the length and breadth of the rectangle.
According to the question
⇒ 30 = 2(2b + b)
⇒ 30 = 2(3b)
⇒ 30 = 6b
⇒ b = $\frac{30}{6}$ = 5 cm
So, length, l = 2b = 2 × 5 = 10 cm
⇒ Diagonal = $\sqrt{l^2 + b^{2}}$ = $\sqrt{100+25}$ = $\sqrt{125}$ = 5$\sqrt{5}$
Hence, the correct answer is $5\sqrt{5} \text{ cm}$.
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