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The length of the rectangular slab = L

The width of the rectangular slab = W

The formula for perimeter in terms of the length and width is 2L + 2W = 60

The area =L*W = 224

So L=224/W

We substitute that into the formula for perimeter and we have

P=2(224/w)+2w=60

This can be simplified to

w2-30w+224=0 so we can solve it and find w.

Fortunately, it factors or else we would need to use the quadratic equation.

(w-14)(w-16)=0. Now we use the zero product rule and we find

the solutions are 14 and 16. This means the rectangle is 14x16. We need to check the answer.

We note that 14x16=224 so that is the desired area and 14x2+16x2=28+32=60 which is the desired perimeter.

Q: What is the length and width of a rectangle with the perimeter of 60 and an area of 224?

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The area is the length times the width. The perimeter is two times the length plus two times the width.

The area is the length times the width. The perimeter is two times the length plus two times the width.

64 meters

Important to note are these formulae: Perimeter_of_rectangle = 2 x (length + width) Area_of_rectangle = length x width So if the perimeter and area are known, then: 2 x (length + width) = perimeter => length + width = perimeter / 2 => length = perimeter / 2 - width length x width = area => (perimeter / 2 - width) x width = area (substituting for length given above) => perimeter / 2 x width - width2 = area => width2 - perimeter / 2 x width + area = 0 which is a quadratic and can be solved either by factorization or by using the formula: width = (perimeter / 2 +/- sqrt(perimeter2 / 4 - 4 x area)) / 2 = (perimeter +/- sqrt(perimeter2 - 16 x area)) / 4 This will provide two values for the width. However, each of these values is the length for the other, so the larger value is the length and the smaller value is the width. Sometimes only 1 value will be found for the width above. In this case, the rectangle is actually a square which means that the length and width are both the same. Examples: 1. perimeter = 6, area = 2 width2 - perimeter / 2 x width + area = 0 => width2 - 6 / 2 x width + 2 = 0 => width2 - 3 x width + 2 = 0 => (width - 2) x (width - 1) = 0 => width = 2 or 1. So the length is 2 and the width is 1. 2. perimeter = 12, area = 9 width2 - perimeter / 2 x width + area = 0 => width2 - 12 / 2 x width + 9 = 0 => width2 - 6 x width + 9 = 0 => (width - 3)2 = 0 => width = 3 So the rectangle is a square with both length and width of 3.

28

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