Question

a rectangle with one side of length 4cm is inscribed in a circle of diameter 5 cm.find the area of the rectangle.

Answer 1

Let the area be x.

Then it will be x^2 + 4^2 = 5^2

                        x^2 + 16 = 25

                       x^2 = 9

                        x = 3.

Area of the rectangle will be 3×4 = 12 cm^2.

Answer 2

Given,

Radius of circle = 2.5 cm

Diameter = 2*r  = 5 cm

Here, Diameter of rectangle = Diagonal of rectangle = 5 cm

Hence, Sides of triangle formed = 4 cm and 5 cm and x cm

We know,

Pythagoras Theorem ,

i.e H² = B² + P²

5² = x² + 4²

25 = x² + 16

9 = x²

3 = x

Hence sides of rect. = 3 cm, 4 cm

Area = l*b

       = 3*4

       = 12 cm²

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