Question

A plan for a house includes rectangular room with an area of 60 square meters and a perimeter of 32 meters. What are the length and width of the room?

Answer 1

When width of room is 6 meters then length is 10 meters

When width of room is 10 meters then length is 6 meters.

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)

⇒
`32=2((60)/(y) )+2y`

⇒
`32=(120)/(y) +2y`

⇒
`32=(120 + 2y^(2) )/(y)`

⇒
`32y= 120 + 2y^(2)`

⇒
`120 + 2y^(2)- 32y = 0`

⇒
`60 + y^(2)- 16y = 0`

⇒
`y^(2)- 16y+60  = 0`

⇒
`y^(2)- 10y-6y+60  = 0`

⇒
`y(y-10)-6(y-10)= 0`

⇒
`(y-6) (y-10)= 0`

⇒ 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

⇒
`(60)/(6) =x`

⇒
`10 =x`

When y = 10

⇒
`(60)/(10) =x`

⇒
`6 =x`

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.