Respuesta :
Answer:
When width of room is 6 meters then length is 10 meters
When width of room is 10 meters then length is 6 meters.
Step-by-step explanation:
Given : The area of rectangular room is 60 square meters .
The Perimeter of room is 32 meters.
To Find : Length and width of room
Solution :
Let length of room be x meters
Let width of room be y meters.
Now , Formula of area of rectangle is:
Area of rectangle = Length * Width
Since we are given that area of rectangular room is 60 square meters .
⇒ 60 = x * y ----(a)
Now Formula of perimeter of rectangle is :
Perimeter of rectangle = 2(length + width)
Since we are given that Perimeter of room is 32 meters.
⇒32 = 2(x+y)
⇒32= 2x+2y ----(b)
Now substitute the value of x from (a) in (b)
⇒[tex]32=2(\frac{60}{y} )+2y[/tex]
⇒[tex]32=\frac{120}{y} +2y[/tex]
⇒[tex]32=\frac{120 + 2y^{2} }{y} [/tex]
⇒[tex]32y= 120 + 2y^{2} [/tex]
⇒[tex] 120 + 2y^{2}- 32y = 0 [/tex]
⇒[tex] 60 + y^{2}- 16y = 0 [/tex]
⇒[tex] y^{2}- 16y+60 = 0 [/tex]
⇒[tex] y^{2}- 10y-6y+60 = 0 [/tex]
⇒[tex] y(y-10)-6(y-10)= 0 [/tex]
⇒[tex] (y-6) (y-10)= 0 [/tex]
⇒ y-6=0 and y-10=0
⇒ y=6 and y =10
Now calculate value of x corresponding to these value of y by putting values of y in a
When y = 6
⇒[tex]\frac{60}{6} =x[/tex]
⇒[tex]10 =x[/tex]
When y = 10
⇒[tex]\frac{60}{10} =x[/tex]
⇒[tex]6 =x[/tex]
So, when y= 6 then x= 10 and when y= 10 then x = 6
Thus when width of room is 6 meters then length is 10 meters
Thus when width of room is 10 meters then length is 6 meters.
