The length of a rectangle is 10 cm more than the side of a square and its breadth is 8 cm less than the side of the square. If the areas of both the rectangle and square are equal, then what will be the perimeter (in cm) of the rectangle?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 164
Formula Used:
Area of ectangle = l × b
Area of square = a2
Perimeter of rectangle = 2(l + b)
Explanation:
LEt the side of the square be x cm.
According to the given question,
Length of rectangle = (x + 10) cm
Breadth of rectangle = (x - 8) cm
Now, (x + 10) × (x - 8) = x2
⇒ x2 + 2x - 80 = x2
⇒ 2x - 80 = 0
⇒ 2x = 80
⇒ x = 40
Now, length = (x + 10) = 40 + 10 = 50 cm
Breadth = (x - 8) = 40 - 8 = 32 cm
So, Perimeter = 2(50 + 32) = 2 × 82 = 164 cm
Hence the required answer is 164 cm.