Mathematics

Question

A piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide. What is the area of the reduced carpet?

2 Answer

  • Answer:

    [tex]\text{Area of reduced carpet}=6\text{ ft}^2[/tex]

    Step-by-step explanation:

    We have been given that a piece of carpet is 8 feet wide and 12 feet long. The carpet needs to be reduced by a scale factor so that the reduced carpet is 2 feet wide.

    First of all, let us find the scale factor by which the width of carpet has been reduced.

    [tex]\text{Original width of carpet}\times \text{Scale factor}=2\text{ ft}[/tex]

    [tex]\text{8 ft}\times \text{Scale factor}=2\text{ ft}[/tex]

    Dividing both sides by 8 ft we will get,

    [tex]\frac{\text{8 ft}\times \text{Scale factor}}{\text{8 ft}}=\frac{2\text{ ft}}{\text{8 ft}}[/tex]

    [tex]\text{Scale factor}=\frac{1}{4}[/tex]

    Let us find the length of carpet after reduced by a scale factor of [tex]\frac{1}{4}[/tex].

    [tex]\text{Length of the carpet after reducing a factor of }\frac{1}{4}=12\text{ ft}\times \frac{1}{4}[/tex]

    [tex]\text{Length of the carpet after reducing a factor of }\frac{1}{4}=3\text{ ft}[/tex]

    Now we will multiply the reduced length and width of carpet to find the area of reduced carpet.

    [tex]\text{Area of reduced carpet}=2\text{ ft}\times 3\text{ ft}[/tex]

    [tex]\text{Area of reduced carpet}=6\text{ ft}^2[/tex]

    Therefore, the area of reduced carpet is 6 square feet.

  • Answer: Hello there!

    initially, the carpet was 8ft wide and 12ft long.

    The rescaled carpet has 2ft wide.

    The scale factor then is: 8ft*k = 2ft

    k = 2ft/8ft = 1/4

    now that we know the scale factor, we can find the length of the long side in the rescaled carpet:

    x = 12ft*(1/4) = 3ft

    Then, the rescaled carpet is 2ft wide and 3ft long.

    The area of the square is equal to the product between the wide length and the length of the long side; so:

    A = 2ft*3ft = 6ft^2

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