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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 if both the rectangle and square are equal, then what will be perimeter (in cm) of the rectangle?

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 if both the rectangle and square are equal, then what will be perimeter (in cm) of the rectangle? Correct Answer 164

Given:

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

Formula used:

Area of square = a2

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

Calculation:

Let the side of square be a 

According to the question

⇒ (a + 10)(a – 8) = a2

⇒ 2a – 80 = 0

⇒ 2a = 80

⇒ a = 40 cm

Now,

Length of rectangle = a + 10 = (40 + 10) = 50 cm

Breadth of rectangle = a – 8 = (40 – 8) = 32 cm

Perimeter of rectangle = 2(l + b)

⇒ 2(50 + 32)

⇒ 2 × 82 cm

⇒ 164 cm

∴ The perimeter of rectangle is 164 cm

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