Question : If the length of one side and the diagonal of a rectangle are 7 cm and 25 cm, respectively, then find its perimeter (in cm).
Option 1: 124
Option 2: 36
Option 3: 62
Option 4: 72
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Correct Answer: 62
Solution :
Given: The length of one side and the diagonal of a rectangle are 7 cm and 25 cm.
The perimeter and breadth of the rectangle are given as $2(L + B)$ and $D^2= B^2+L^2$, respectively, where $L$ is the length, $B$ is the breadth, and $D$ is the diagonal.
⇒ ${25}^2= B^2+7^2$
⇒ $625= B^2+49$
⇒ $625-49= B^2$
⇒ $B^2=576$
$\therefore B= 24$ cm
⇒ The perimeter of the rectangle = 2(7 + 24) = 62 cm
Hence, the correct answer is 62.
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