Length

[Guest]

A floor is to be covered with carpet. Length is four times width. If floor was two feet larger each way, fifty six sq. yds. more would be needed. Determine length.

Unsure how to solve.

[Guest]

Let's denote the width of the original floor as ww (in feet).
Since the length is four times the width, the length LL would be 4w (in feet).

The area of the original floor is [tex]Area_1=L×w=(4w)×w=4w^2[/tex] square feet.

If the floor was extended by two feet in each direction:
The new length would be 4w+2 eet.
The new width would be w+2 feet.

The area of the extended floor would be [tex]Area_2=(4w+2)(w+2)=4w^2+2w+8w+4=4w^2+10w+4[/tex] square feet.

The difference in the area of the extended and original floors is 56 square yards, but we need to convert this into square feet for consistency.

There are 9 square feet in 1 square yard. So, 56 square yards would be 56×9=504 square feet.

Thus, we can set up the equation:
[tex]Area_2−Area_1=504[/tex]

(4w2+10w+4)−(4w2)=504

10w+4=504

10w=500

w=50

So, the width of the original floor is 50 feet.

Now, we can find the length:
L=4w=4(50)=200 feet.

Therefore, the original length of the floor is 200 feet.

[Guest]

Ok, Thanks.

[Guest]

Let's use "w" to represent the width of the original floor in feet. Given that the length is four times the width, we denote the length as 4w.

The area of the original floor is calculated as the product of length and width: L × w = (4w) × w = 4w^2 square feet.

If we extend the floor by two feet in each direction, the new length becomes 4w + 2 feet and the new width becomes w + 2 feet.

The area of the extended floor can be expressed as (4w + 2) × (w + 2) = 4w^2 + 2w + 8w + 4 = 4w^2 + 10w + 4 square feet.

To find the difference in area between the extended and original floors, we convert 56 square yards to square feet by multiplying by 9 (since 1 square yard equals 9 square feet), resulting in 504 square feet.

Setting up the equation (Area2 - Area1 = 504), we have:
(4w^2 + 10w + 4) - (4w^2) = 504
10w + 4 = 504
10w = 500
w = 50

Therefore, the width of the original floor is 50 feet. To find the length, we multiply the width by 4: L = 4w = 4(50) = 200 feet.

Thus, the original length of the floor is 200 feet.

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[Guest]

Ok, Thanks.