Find the perimeter of the triangle ABC is (s-a)=10cm, (s-b)=12cm and (s-c)=8cm where s is the semi perimeter of triangle ABC
Answers
Answer:
Answer: The answer is 11 cm, 6 cm and 15 cm.
Step-by-step explanation: We are given to find the values of a, b and c, where these three represents the sides of a triangle.
We know that if a, b and c are the three sides of a triangle, then 's' is defined by
s=\dfrac{a+b+c}{2}.s=
2
a+b+c
.
From the given information, we have
\begin{gathered}s-a=5\\\\\Rightarrow \dfrac{a+b+c}{2}-a=5\\\\\Rightarrow b+c-a=10~~~~~~~~~~~~~~~~(A)\end{gathered}
s−a=5
⇒
2
a+b+c
−a=5
⇒b+c−a=10 (A)
Similarly, we find that
\begin{gathered}c+a-b=20~~~~~~~~~~~~~~~~(B)\\\\a+b-c=2.~~~~~~~~~~~~~~~~~(C)\end{gathered}
c+a−b=20 (B)
a+b−c=2. (C)
Adding equations (A) and (B), we have
\begin{gathered}2c=30\\\\\Rightarrow c=15.\end{gathered}
2c=30
⇒c=15.
Adding equations (B) and (C), we have
\begin{gathered}2a=22\\\\\Rightarrow a=11.\end{gathered}
2a=22
⇒a=11.
From equation (A), we get
\begin{gathered}b+15-11=10\\\\\Rightarrow b=6.\end{gathered}
b+15−11=10
⇒b=6.
Thus, a = 11 cm, b = 6 cm and c = 15 cm.
Solution
Given :-
- In triangle ABC (S - a ) = 10 cm , (S - b) = 12 cm, (S - c) = 8 cm
- S is semi perimeter of triangle
Find :-
- Perimeter of triangle
Explanation
We Know,
★ Semi perimeter = (a + b + c)/2
Where,
- a = AB
- b = BC
- c = CA
So, Now
case 1.
==> S - a = 10
==> a = S - 10________(1)
Similarly
Case 2.
==> b = S - 12 ________(2)
case 3.
==> c = S - 8 ________(3)
So Now
==> S = (a + b + c)/2
Keep value of a , b & c
==> S = [(S - 10)+(S-12)+(S-8)]/2
==> 2S = 3S - 30
==> S = 30
That's mean
==> (a + b + c)/2= 30
==> a + b + c = 30 × 2
==> a + b + c = 60
That's mean,
Sum of all side of a triangle = ( AB)+(BC)+(CA) = a + b + c = Perimeter of triangle
Hence
- perimeter of triangle will be = 60 cm