Question

find area of a triangle given perimeter 32 cm and one side 11 centimetre and difference of other two sides is 5cm

Answer 1

let the sides of triangle be ab , bc , ca respectively
ab + bc + ca = perimeter of triangle

=> let ab = 11 cm
perimeter = 32 cm
and bc -ca = 5 cm
=> bc = 5+ca

ab+bc+ca = 32
=> 11+5+ca+ca = 32
=> 16+2ca = 32
=> 2ca = 32-16 = 16
=> ca = 16/2 = 8 cm


bc = 5+ca
=> bc = 5+8 => 13 cm

ab = 11 cm
bc = 13 cm
ca = 8 cm


hope this helps

Answer 2

Given,
One side of triangle = 11 cm.
Let the second side be x
Then the third side be x -5

Perimeter = 32

We know that,

11+x + x - 5 = 32

2 x = 32-6

2 x = 26

x =13.


Therefore, Other sides are 13,8.

We know semiperimeter = 32/2 = 16.

Area = √(s-a)(s-b)(s-c)

=√(16-11)(16-13)(16-8)

=√5*3*8

=√120

=2√30 cm²