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QuestionA rectangular room's width is 2 times its length, with a perimeter of 28 m. Find the dimensions rounded to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The room is rectangular. The width of the room is times its length3. The perimeter of the room is28 meters4. We are asked to find the dimensions of the room (length and width) and round to the hundredths place

STEP 2

The perimeter of a rectangle is given by the formulaPerimeter=2(Length+Width)Perimeter =2(Length + Width)

STEP 3

We know that the width is2 times the length, so we can substitute this into the formulaPerimeter=2(Length+2×Length)Perimeter =2(Length +2 \times Length)

STEP 4

implify the equationPerimeter=2(3×Length)Perimeter =2(3 \times Length)

STEP 5

Now, plug in the given value for the perimeter to solve for the length28=2(3×Length)28 =2(3 \times Length)

STEP 6

olve the equation for LengthLength=28/(2×3)Length =28 / (2 \times3)

STEP 7

Calculate the lengthLength=28/6=4.67 metersLength =28 /6 =4.67 \, meters

STEP 8

Now that we have the length, we can find the width by multiplying the length by2Width=2×LengthWidth =2 \times Length

STEP 9

Plug in the value for the length to calculate the widthWidth=2×4.67Width =2 \times4.67

STEP 10

Calculate the widthWidth=2×4.67=9.33 metersWidth =2 \times4.67 =9.33 \, metersThe length of the room is4.67 meters and the width of the room is9.33 meters.

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