Question

The perimeter of a triangle is 54 cm. One side of a triangle is 22 cm longer than the smallest side and the third side is 1 cm less than 9 times the smallest side. Find the area of the triangle.

Answer 1

Answer:

Step-by-step explanation:   Let the sides be x,y and z

then perimeter is sum of all sides

so,x+y+z=54

let the smallest side be x

then equations are =>

y=x+22

z= 9(x)-1

now replacing the values of y and z in the above equation =>

x+y+z=54

x+(x+22)+(9(x)-1)=54

x+x+22+9x-1=54

11x+21=54

11x=54-21

11x=33

x=3

now putting values,

y=x+22

y=25

and

z=9x-1

z=26

now using herons formula ,

area=$\sqrt{s(s-x)(s-y)(s-z)}$

area=$\sqrt{27*24*2*1}$

area=36 cm^2