Algebra word problem related to area

Question

A square filed has an area of 479 ft². What is the approximate length of a side of the filed? Give your answer to the nearest foot. Explain your response.

My son is homeschooled and this is one of the questions on his math. I am not looking for the above answer just need to know how to better explain it too him so that he understands how to work this problem out, so that he is better prepared for his unit test.

Answer 1

To find the area of a square or rectangle, you need to multiply the length and width (which is why the area is to the second power). For this problem in particular, you need to work backwards and use the area to find the length and width. The shape being a square makes things easier because the length and width are identical and less steps are required.

We can say Area = Length * Width or Area = L² because we're finding the sides of a square.

479 ft² = L²

From here, square root both sides to find the approximate length of each side.

Because the problem is asking to round to the nearest foot, you will want to round up for decimals 0.5 and higher or round down for decimals below 0.5. The exception to this way of rounding would be if a problem explicitly says to round up or down.

I hope this helps and if you need any further help for your son's Math please feel free to contact me.

Answer 2

The way the question is written it seems the area of 479 ft² is for a square-shape. A square means all 4 sides are of equal length. Area is calculated as length*width of a 2-dimensional figure, but for a square length = width, so area is the same as length*length, or length².

To find the length of a square with a given area, simply find the square root of the area. Here area = 479 ft², so the length of the square is sqrt(479) ~ 21.886 ft. To the nearest foot this becomes 22 ft.

Answer 3

479 square feet is the area of the square field

a square has all four sides equal in length

you want a number multiplied by itself to give you 479

there is a mathematical process but it is very lengthy, time-consuming and outdated

so we use a calculator or if you can't use a calculator you use trial and error

seeing that you want the answer to the nearest foot, this makes the work easier

20*20=400 too small

21*21=441 too small

22*22=484 to large

which number, 441 or 484 is closest to 479 ?

484-479=5

479-441=38

484 is

the answer is 22 feet

if you wanted more accuracy...

21.5*21.5=462.25

21.6*21.6=466.56

21.7*21.7=470.89

21.8*21.8=475.24

21.9*21.9=479.61

we use 21.8

21.85*21.85=477.4225

21.86*21.86=477.8596

21.87*21.87=478.2969

21.88*21.88=478.7344

21.89*21.89=479.1721

we use 21.88

now try 21.885*21.885 and continue on until you get the accuracy needed