Answer:
L=22 m or L=9 m
Step-by-step explanation:
We are given that
Perimeter of rectangle=62 m
Area of rectangle =[tex]1980000cm^2=198m[/tex] (1m=100 cm)
We have to find the lengths of its sides.
Let Length of rectangle =x
Breadth of rectangle=y
Perimeter of rectangle=2(x+y)
Area of rectangle =xy
According to question
[tex]2(x+y)=62[/tex]
[tex]x+y=\frac{62}{2}=31[/tex]
[tex]xy=198[/tex]
[tex]y=\frac{198}{x}[/tex]
Substitute the value of y
[tex]x+\frac{198}{x}=31[/tex]
[tex]\frac{x^2+198}{x}=31[/tex]
[tex]x^2+198=31x[/tex]
[tex]x^2-31x+198=0[/tex]
[tex]x^2-22x-9x+198=0[/tex]
[tex]x(x-22)-9(x-22)=0[/tex]
[tex](x-22)(x-9)=0[/tex]
[tex]x-22=0\implies x=22[/tex]
[tex]x-9\implies x=9[/tex]
Substitute the value x=22
[tex]y=\frac{198}{22}=9[/tex]
Substitute the value of x=9
[tex]y=\frac{198}{9}=22[/tex]
Hence, the length of sides of rectangle are
x=22 m and x=9 m
