The area of a square and rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 10 cm and the breadth is less than 5 cm. The perimeter(in cm) of the rectangle is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 50.
We know that,
Area of rectangle = Length × Breadth
Area of square = (Side)2
Perimeter of rectangle = 2(Length + Breadth)
Now, according to the question
Let the side of a square be s
Let the Length and Breadth of a rectangle be I & b respectively
⇒ s2 = (l × b)
⇒ s2 = [(s + 10) × (s - 5)]
⇒ s2 = s2 - 5s + 10s - 50
⇒ 5s = 50
⇒ s = 10
⇒ I = (s + 10) = 20
⇒ b = (s - 5) = 10 - 5 = 5
Perimeter of Rectangle = 2(20 + 5) = 50
Thus, Perimeter of Rectangle = 50 cm