Question

A triangular park of dimensions 5 m, 12 m, and
13 m is constructed with a circular playground
within the park. If the circle occupies the
maximum possible area, what will be the radius
(in m) of the circular playground?​

Answer 1

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Answer 2

The radius of the circular playground is 6.5.

Given,

The dimensions of the triangular park are 5 m, 12 m, and 13 m.

A circle occupies the maximum possible area.

To Find,

The radius of the circle.

Solution,

The given dimensions of the triangle are 5 m. 12 m and 13 m.

From here we can observe that the given triangle is right-angled as its dimensions hold for Pythagoras theorem.

13² = 12²+5²

169 = 169

Now, for a circle to cover the maximum area the circle will circumscribe the triangle. Now, a right angles triangle is circumscribed in a circle so, its hypotenuse will be the diameter of the circle.

So,

Radius of the circle = 13/2 = 6.5 m.

Hence, the radius of the circular playground is 6.5 m.