Find the inradius (approximate value) of the triangle having sides 12

1.	Find the inradius (approximate value) of the triangle having sides 12 cm, 16 cm and 22 cm.1. 3.7 cm2. 6.7 cm3.1.5 cm4. 7.3 cm
Answer» Correct Answer - Option 1 : 3.7 cm Given: Sides of triangles are 12 cm, 16 cm, and 22 cm Formula used: Area of triangle = \(\sqrt {s\left( {s\; - \;a} \right)\left( {s\; - \;b} \right)\left( {s\; - \;c} \right)} \) Here, s is semi perimeter, and a, b, and c are sides of the triangle Inradius = Area/s Calculation: Let a be 12 cm, b be 16 cm, and c be 22 cm Semi perimeter (s) = (12 + 16 + 22)/2 ⇒ s = 50/2 = 25 Area of triangle = \(\sqrt {s\left( {s\; - \;a} \right)\left( {s\; - \;b} \right)\left( {s\; - \;c} \right)} \) ⇒ Area of triangle = \(\sqrt {25\left( {25\; - \;12} \right)\left( {25\; - \;16} \right)\left( {25\; - \;22} \right)} \) ⇒ Area of triangle = \(\sqrt {25 \times 13 \times 9 \times 3} \) ⇒ Area of triangle = √8775 cm² ⇒ Area of triangle ≈ 93.67 Inradius = Area/s ⇒ Inradius = 93.67/25 ∴ Inradius is 3.7 cm approximately

Find the inradius (approximate value) of the triangle having sides 12 cm, 16 cm and 22 cm.1. 3.7 cm2. 6.7 cm3.1.5 cm4. 7.3 cm

Answer» Correct Answer - Option 1 : 3.7 cm

Given:

Sides of triangles are 12 cm, 16 cm, and 22 cm

Formula used:

Area of triangle = \(\sqrt {s\left( {s\; - \;a} \right)\left( {s\; - \;b} \right)\left( {s\; - \;c} \right)} \)

Here, s is semi perimeter, and a, b, and c are sides of the triangle

Inradius = Area/s

Calculation:

Let a be 12 cm, b be 16 cm, and c be 22 cm

Semi perimeter (s) = (12 + 16 + 22)/2

⇒ s = 50/2 = 25

Area of triangle = \(\sqrt {s\left( {s\; - \;a} \right)\left( {s\; - \;b} \right)\left( {s\; - \;c} \right)} \)

⇒ Area of triangle = \(\sqrt {25\left( {25\; - \;12} \right)\left( {25\; - \;16} \right)\left( {25\; - \;22} \right)} \)

⇒ Area of triangle = \(\sqrt {25 \times 13 \times 9 \times 3} \)

⇒ Area of triangle = √8775 cm²

⇒ Area of triangle ≈ 93.67

Inradius = Area/s

⇒ Inradius = 93.67/25

∴ Inradius is 3.7 cm approximately