Question

Peter wants to add a room to his house using a ratio of 9 to 4 for its dimensions. He will make the length of the room 17 feet. How wide will the room be to the nearest foot?

Answer 1

The width of the room to nearest foot
`\approx` 8 feet

Explanation:

Ratio of length to width of the room Peter wants to add to his house = 9:4

Given length of the room = 17 feet

To find the width of the room.

Solution:

From the given data we know that the length and width of the room bear a common ratio which is 9:4

Let width of the room in feet be =
`w`

Thus, the ratio can be given as:

⇒
`(Length)/(Width)=(9)/(4)`

Plugging in length of room in the equation = 17 feet.

Solving for
`w`

⇒
`(17)/(w)=(9)/(4)`

Multiplying both sides by 4.

⇒
`4*(17)/(Width)=(9)/(4)*4`

⇒
`(68)/(w)=9`

Multiplying both sides by
`w`

⇒
`w*(68)/(w)=9* w`

⇒
`68=9w`

Dividing both sides by 9.

⇒
`(68)/(9)=(9w)/(9)`

∴
`w=7.55\approx 8`

Thus, the width of the room to nearest foot
`\approx` 8 feet