Question

What is the largest area of rectangle formed by two perpendicular diameters and a point on the circle of diameter 20 √2 cm​

Answer 1

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Step-by-step explanation:

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Answer 2

Given :

Diameter of the circle 'd' = 20$\sqrt{2\\}$ cm

To find :

Area of the largest rectangle formed by the two perpendicular diameters.

Solution :

• The largest rectangle within the circle formed from the perpendicular diameters will be a square.
• The diagonals of this square will be the diameters of the circle.

• We have diameter 'd' = 20$\sqrt{2\\}$ cm

• If we divide the square into two triangles, we get two right isosceles triangles each having a hypotenuse = 20$\sqrt{2}$ cm

In an isosceles triangle;

When hypotenuse = 20$\sqrt{2}$ cm,

The length of the other two sides

                    = (20$\sqrt{2}$) / $\sqrt{2}$ cm =  20cm

Isosceles side of the triangle = side of the square = 20cm

Area of the square = (side)² = (20 cm)² = 400 cm²

Thus the area of the largest rectangle formed is 400 cm²