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

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.