1.

The perimeter of a rectangle is 160 m and the difference of two sides is 48 m. Find the side of a square whose area is equal to the area of this rectangle.1). 32 m2). 8 m3). 4 m4). 16 m

Answer»

Let the length and WIDTH of the given rectangle be l and b respectively.

We know that, perimeter of rectangle = 2 × (length + width)

⇒ 160 = 2 × (l + b)

⇒ l + b = 80 m …(1)

Given, difference of two sides = 48 m

∴ l – b = 48 …(2)

SOLVING above two EQUATIONS we get,

l = 64 meters & b = 16 meters

We know that, Area of rectangle = l × b

Let the side of the square be ‘a’ meters. Thus, according to the question

⇒ a2 = l × b [?Area of square = side2]

⇒ a2 = 64 × 16

⇒ a = 32 meters


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