The semi perimeter of a triangle exceeds each of its side by 5, 3 and 2 respectively. What is the perimeter of the triangle?
The semi perimeter of a triangle exceeds each of its side by 5, 3 and 2 respectively. What is the perimeter of the triangle?
A) 10
B) 20
C) 15
D) 12
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Correct option is (B) 20
Let sides of triangle are a, b & c.
\(\therefore\) S \(=\frac{a+b+c}2\)
\(\Rightarrow\) a+b+c = 2S __________(1)
Let S = a+5, __________(2)
S = b+3, __________(3)
S = b+2 __________(4) (According to given conditions)
By adding (2), (3) & (4), we get
3S = (a+b+c) + (5+3+2)
\(\Rightarrow\) 3S = 2S + 10 (From (1))
\(\Rightarrow\) 3S - 2S = 10
\(\Rightarrow\) S = 10
\(\therefore\) Perimeter = 2S
= 2 \(\times\) 10 = 20
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