Question

The area of a rectangle is 10 cm^2. One side of the rectangle is x cm. Express the perimeter of the rectangle in terms of x and show that this rectangle cannot have a perimeter of 12 cm.

Answer 1

Area of rectangle = 10cm²

We know that, Area of rectangle = lb

lb = 10

Let l = x cm. Then b = 10/x cm.

Perimeter of rectangle

$= 2(l + b) \\ = 2(x + \frac{10}{x}) \\ = \frac{2 {x}^{2} + 10 }{x}cm.$

But, this rectangle can't have 12 as its perimeter because Sides have to be factors of 10.If l = 5cm and b = 2cm then it will have perimeter 14cm.If l = 10cm and b = 1cm then it will have perimeter 22cm.

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