Area of a square that is increased by 5 foot?

Question

If two sides of a square field were increased by five feet, the area of the field would increase by 245 ft squared. Find the area of the orginal square. Can anyone tell me how I would solve this problem

Answer 1

You need to set up an equation. Let s be the length of the original square. Therefore s^2 is the area of the original square. You also know that increasing the side by 5 results in an increase in the area by 245 so (s+5)^2 = s^2 + 245 this works out to s^2 + 10s + 25 = s^2 + 245. Cancel the s^2 terms and move the 25 to the other side and you get 10s = 220 or s = 22. Hence the area of the original square is s^2 = 22^2 = 484.

Answer 2

You could call the old side S.
The new side would be S+5

The old area is S squared or S^2
The new area is (S+5) squared. or (S+5)^2
The difference in areas is 245 which = (S+5)^2 - S^2

Multiply out the terms and add them=
S^2+10S+25-S^2 = 245.
Notice that you have S^2-S^2 so that S^2 goes away
Next 10S+25=245 so 10S = 245-25 = 220
10S=220 so S=220/10 = 22 which is the original size of the side.

Multiply SxS = 22x22 = 484 sq ft

Answer 3

Let x = side of the square:

(x + 5)(x + 5) = x^2 + 245
x^2 + 5x + 5x + 25 = x^2 + 245
10x = 220
x = 22

Area of the original square:
= 22^2
= 484

Proof:
(22 + 5)^2 = 22^2 + 245
27^2 = 484 + 245
729 = 729

Answer 4

We are adding a rectangle of area 5*L (L is the side of the original square)

We are told the area added, so

5*L = 245

The original square as a side of L = 245/5 = 49
and an area of 49^2 = 2401

(I refuse to use those units! :-)

Answer 5

let the side of the original square be xft, then
(x+5)^2=x^2+245
x^2+10x+25=x^2+245
10x=220
x=22ft.
area of the original square
=22^2=484 ft^2

Answer 6

It depends on which two sides. Is it two opposite sides, forming a rectangle? Or is it two adjacent sides, forming a figure with only one right angle? In order for it to remain a square, all four sides would have to increase the exact same amount.

Answer 7

Next time, Do your own homework.

http://www.mathopenref.com/squarearea.html

http://www.aaamath.com/B/geo78_x4.htm

:)!