Question

the semi perimeter of a triangle of 10cms. If one of its sides is 5cm and 7 cms respectively then it's third side is ___________​

Answer 1

Given : semi perimeter of a triangle of 10 cms.

Two of its sides is 5cm and 7 cms respectively

To Find :   third side  

Solution:

A triangle with three side a , b & c

semi perimeter  s = (a + b + c)/2

s = 10

a = 5

b = 7

c = ?

=> 10  =  (5 + 7 + c)/2

=> 20 = 12 + c

=> c = 8

third side of triangle is 8 cm

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Answer 2

SOLUTION

GIVEN

• The semi perimeter of a triangle of 10 cm

• Two of its sides is 5 cm and 7 cm respectively

TO DETERMINE

The third side

CONCEPT TO BE IMPLEMENTED

1. Perimeter of a triangle is sum of the three sides

2. Semi perimeter is half the perimeter

EVALUATION

Here it is given that the semi perimeter of a triangle of 10 cm

∴ Perimeter = 2 × 10 = 20 cm

Now Two of its sides is 5cm and 7 cm respectively

So by the given condition

5 cm + 7 cm + Third side = 20 cm

$\implies \sf{12 \: cm +Third \: side = 20 \: cm }$

$\implies \sf{Third \: side = 20 \: cm -12 \: cm }$

$\implies \sf{Third \: side = 8 \: cm }$

FINAL ANSWER

Hence the required third side = 8 cm

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