The area of a rectangle is the product of its length and width. The area of the rug when reduced by one-fifth is 5 ft².
The area of a rectangle is the product of its length and width. It is written as,
[tex]\rm \text{Area of rectangle} = Length \times Width[/tex]
As we need to reduce the rug by one-fifth, therefore, we will need to reduce the dimensions of the rug by one-fifth, because the scale factor is always applicable to the dimensions. Therefore, the dimensions of the rug are,
[tex]\rm Length_{new} = 12.5 \times \dfrac{1}{5} = 2.5\ ft[/tex]
[tex]\rm Width_{new} = 10 \times \dfrac{1}{5} = 2\ ft[/tex]
Thus, the area of the rug when reduced by one-fifth can be written as,
[tex]\rm \text{Area of rectangle} = Length \times Width[/tex]
[tex]= 2.5 \times 2 \\\\= 5\rm\ ft^2[/tex]
Hence, the area of the rug when reduced by one-fifth is 5 ft².
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