Question

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is ______.

विकल्प

• r² sq.units

• r²

• 2r²

• `1/2 "r"^2` sq.units

• 2r² sq.units

• r³

• `sqrt(2)"r"^2` sq.units

• 2r³

Answer 1

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is r² sq.units.

Explanation:

The largest triangle that can be inscribed in a semi-circle of radius r units is the triangle having its base as the diameter of the semi-circle and the two other sides are taken by considering a point C on the circumference of the semi-circle and joining it by the endpoints of diameter A and B.

∴ ∠C = 90°  ...(By the properties of circle)

So, ΔABC is right-angled triangle with base as diameter AB of the circle and height be CD.

Height of the triangle = r

∴ Area of largest ΔABC = `1/2 xx "Base" xx "Height"`

= `1/2 xx "AB" xx "CD"`

= `1/2 xx 2"r" xx "r"`

= r² sq.units