Math

QuestionWhat is the floor area in ft2\mathrm{ft}^{2} if it needs 25.4 square yards of carpet? (3ft=1yd)(3 \mathrm{ft}=1 \mathrm{yd})

Studdy Solution

STEP 1

Assumptions1. The area of the room is25.4 square yards. The conversion factor is1 yard =3 feet

STEP 2

We need to convert the area from square yards to square feet. To do this, we need to square the conversion factor.
1yd2=(ft)21\, \mathrm{yd}^{2} = (\, \mathrm{ft})^{2}

STEP 3

Calculate the square of the conversion factor.
1yd2=9ft21\, \mathrm{yd}^{2} =9\, \mathrm{ft}^{2}

STEP 4

Now that we have the conversion factor in square units, we can use it to convert the area of the room from square yards to square feet.
Areainft2=Areainyd2×ConversionfactorArea\, in\, \mathrm{ft}^{2} = Area\, in\, \mathrm{yd}^{2} \times Conversion\, factor

STEP 5

Plug in the given area and the conversion factor to calculate the area in square feet.
Areainft2=25.4yd2×9ft2/yd2Area\, in\, \mathrm{ft}^{2} =25.4\, \mathrm{yd}^{2} \times9\, \mathrm{ft}^{2}/\mathrm{yd}^{2}

STEP 6

Calculate the area in square feet.
Areainft2=25.4yd2×9ft2/yd2=228.6ft2Area\, in\, \mathrm{ft}^{2} =25.4\, \mathrm{yd}^{2} \times9\, \mathrm{ft}^{2}/\mathrm{yd}^{2} =228.6\, \mathrm{ft}^{2}The area of the room is228.6 square feet.

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