Question

The difference between the semiperimeter and the sides of a triangle ABC are 3 cm, 17 cm and 34 cm
respectively. Find the area of triangle.​

Answer 1

let consider sides of a triangle are a,b,c respectively.

we know that semi perimeter of a triangle = a+b+c/2

according to given condition,

(a+b+c/2)-a=3

b+c-a=6-(1 st equation)

(a+b+c/2)-b=17

a+c-b=34-(2 nd equation )

(a+b+c/2)-c=34

a+b-c=64-(3red equation)

by solving 1,2,3 equations

a=49,b=35,c=20

Area of triangle =sqrt(s(s-a)(s-b)(s-c)) ( where s is semi perimeter)

=sqrt(52(3)(17)(34))

=300.27 cm^2

Answer 2

Step-by-step explanation:

Given s−a=8cm⋯(1)

s−b=7cm⋯(2)

s−c=5cm⋯(3)

Where a, b, c are sides of triangle

s

2

is 1 semi perimeter ie s=

2

a+b+c

(1) + (2) + (3)

⇒3s−(a+b+c)=20cm

⇒3s−(25)=20cm

⇒s=20cm

Area of triangle =

s(s−a)(s−b)(s−c)

=

20(8×7×5)

=

5600

=20

14

=59cm

solution