Question

Find the area of the triangle having perimeter 32cm. One side of its side is 11cm and difference of the other two sides is 5cm

Answer 1

Answer:

44 cm²

Step-by-step explanation:

Let the sides of the triangle be x,y,z.

Given:

Perimeter of a triangle = 32 cm

x + y + z = 32 cm

And also given that,

one of the sides = 11cm

11 + y + z = 32

y + z = 32 - 11

y + z = 21 -- equation (1).

given that,

y - z = 5 -- equation (1)

Add both the equations,

y + z + y - z = 21 + 5

2y = 26

y = 26/2

y = 13

Substitute "y" value in equation (1).

y + z = 21

13 + z = 21

z = 21 - 13

z = 8

We know that,

Area of a triangle = √p(p - x) (p - y)(p - z)

= √16(16 - 11)(16 - 13)(16 - 8)

= √16(5)(3)(8)

= √1920

Area of the triangle = 44 cm².