Question

find the radius of a circle if area of triangle ABC 84cm^2
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Answer 1

A triangle has an area of 84 cm2 and a perimeter of 48 cm. Find the radius of the incircle.

1) 7 cm

2) 3.5 cm

3) 4 cm

4) 2.2cm

The correct option about the radius of the incircle is 3) 4 cm.

Given:

A triangle has an area of 84 cm2 and a perimeter of 48 cm.

To Find:

The radius of the incircle.

Solution:

To find the radius of the incircle, we will follow the following steps:

As we know,

The formula for finding the area of the triangle =

$\frac{1}{2} \times base \times height$

The formula for finding the perimeter of the triangle is equal to the sum of the sides of the triangle.

Similarly, the area of a circle is

$\pi {r}^{2}$

Here, r is the radius of the circle.

Also,

The relation between the parameter, area, and radius of the circle inscribed in the triangle is given by:

$area \: = \frac{1}{2} \times r \times perimeter$

Now, putting values of area, perimeter, and radius in the above formula we get,

$84 = \frac{1}{2} \times r \times 42$

$r = \frac{84 \times 2}{42} = 2 \times 2 \: cm = 4cm$

Henceforth, the correct option about the radius of the incircle is 3) 4 cm.

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