The area of a triangle is 15 sq cm and the radius of its incircle is 3 cm. Its perimeter is equal to
Answers
The perimeter of triangle ABC is equal to 10 cm.
Step-by-step explanation:
Given:
Referring to the figure attached below, let’s make some assumptions
ABC be the triangle whose area is given as 15 cm²
An incircle with centre O and radius, r = 3 cm
Construction:
Join the centre of the circle O with each of the vertex of the triangle
Solution:
Required Formula:
- Area of a triangle = ½ * base * height
- Perimeter of a triangle = sum of 3 sides of the triangle
From the figure, we can write that,
Area of ΔABC = Ar(∆AOB) + Ar(∆BOC) + Ar(∆AOC) ….. (i)
Based on the first required formula, we get
Ar(∆AOB) = ½ * r * AB ….. (ii)
Ar(∆BOC) = ½ * r * BC ….. (iii)
Ar (∆AOC) = ½ * r * AC ….. (iv)
Now, substituting (ii), (iii) & (iv) in (i), we get
Area of triangle ABC = [½ * r * AB] + [½ * r * BC] + [½ * r * AC]
Since area = 15 cm² and r = 3 cm
⇒ 15 = ½ * 3 * [AB + BC + AC]
⇒ [AB + BC + AC] = [15*2]/3
⇒ AB + BC + AC = 10 cm ← Perimeter of ∆ABC (can be concluded from the second required formula)
Thus, the perimeter of the given triangle is 10 cm.
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Answer:
10 cm
Step-by-step explanation:
ABC be the triangle whose area is given as 15 cm²
An incircle with centre O and radius, r = 3 cm
By the relation,
area=radius(incircle) * s where, s=(a+b+c)/2
15=3*s
s=5
As, s=(a+b+c)/2
5=(a+b+c)/2
a+b+c=10 cm
As, Perimeter of a Traingle= Sum of its sides=a+b+c=10 cm