Question

Sides of a triangle are 9cm, 12cm
and 15cm.Find the area and the
inradius​

Answer 1

Given :

• Sides of a triangle are 9cm, 12cm
• and 15cm

To find :

• Area of triangle
• inradius

Solution :

We will find area of triangle by using heron's formula.

To find area of triangle by using heron's formula, first find semi perimeter of the triangle.

$\sf \implies s = \dfrac{9 + 12 + 15}{2}$

where , s = semi perimeter

$\sf \implies s = \dfrac{36}{2}$

$\sf \implies s =18$

Now , area is :-

$\sf \implies \sqrt{18(18 - 9)(18 - 12)(18 - 15)}$

$\sf \implies \sqrt{18 \times 9 \times 6 \times 3}$

$\sf \implies \sqrt{2 \times 9 \times 9 \times 2 \times 3 \times 3}$

$\sf \implies 2 \times 9 \times 3$

$\sf \implies 54 \: square \: unit$

Now, we have to find put inradius :-

$\sf \large r = \dfrac{a}{s}$

Where :-

• r = inradius

• a = area of triangle

• s = semi perimeter

$\sf \implies r = \dfrac{54}{18} \: units$

$\sf \implies r = \dfrac{3}{1} \: units$

$\sf \implies r = {3} \: units$

Answer :

• Area of triangle = 54 square units

• inradius = 3 units

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[ refer attachment for rough diagram ]