Question

atmaram tukaram Bhide of Gokuldham socity hires a architect for design garden garden is a rectangle inscribed in a circle than

3x and 2y represent the length and breath of garden than relationship between the variables

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Answer 1

Answer:

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Answer 2

QUESTION:

Atmaram Tukaram Bhide, Secretary of Gokuldham Society hires an architect to design a garden in his society. The garden is in the shape of a rectangle inscribed in a circle of radius 10 m as shown in the given figure.

If 2x and 2y represent the length and breadth of the rectangular part then the relation between the variables is

ANSWER:

For the given length, breadth of the rectangular garden, and radius of the circle, the relation between the variables is x² + y² = 100.

Given,

Refer figure.

A rectangle inscribed in a circle of 10 m,

Length of the rectangle = 2x,

The breadth of the rectangle = 2y.

To find,

The relationship between the variables.

Solution,

Refer figure.

It can be seen here, that a rectangle ABCD (garden) is inscribed in a circle with center O, and has a radius,

OA = 10 m.

It is given that,

AB = CD = 2x,

BC = AD = 2y.

Let OP be a perpendicular from center O, on AB.

As we know that the perpendicular on a chord from the center of a circle, bisects the chord.

So, here we can see,

OP will bisect AB

⇒ AP = x.

Similarly, it can also be observed that,

OP will be half of the BC

⇒ OP = y.

Now, since ΔOAP is a right-triangle, right-angled at P,

Pythagoras theorem can be used to determine the relationship between the variables.

Thus,

$(OA)^2=(AP)^2+(OP)^2$

Substituting the respective values,

$(10)^2=x^{2} +y^{2}$

Rearranging,

$\implies x^{2} +y^{2} =(10)^2$

⇒ x² + y² = 100, which is the required relation.

Therefore, for the given length, breadth of the rectangular garden, and radius of the circle, the relation between the variables is x² + y² = 100.

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