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?
Answer & explanation
Correct answer: option 1
We know that,
Area of square = (Side)2
Area of rectangle = l × b
Perimeter of rectangle = 2(l + b)
The length of rectangle = 10 cm more than the side of square
The breadth of rectangle = 8 cm less than the side of the square
Let the side of square be s
According to the question
= (s + 10)(s – 8) = s2
= 2a – 80 = 0
= 2s = 80
= s = 40 cm
Length = (40 + 10) = 50 cm
Breadth = (40 – 8) = 32 cm
Perimeter of rectangle = 2(l + b)
= 2(50 + 32)
= 2 × 82 = 164 cm