What is the equation for the below problem?

Question

if 2 sides of a sq field were increased by 5 ft, the area of the field would increase by 245 ft. Find the area of the original square.

Answer 1

let x be the length of one side of the square.

Then
(x+5)^2 - x^2 = 245

find x^2

Answer 2

Representation: Let x be the measure of the side of the original square in feet, or ( x=side of orig. square; ft. )

Equation: Since the area of a square is s^2, let us represent it: x^2; now, the new square, which has 2 sides increased by 5, it will then become a rectangle, formula: (l)w, now, let us represent. Let us assume that the 2 width"s" of the rectangle are the ones constant: (x+5)x. Now, let us represent it using the fact that the area increased by 245 ft.: (x+5)x-x^2=245
(x^2+5x)-x^2=245

I read that you were asking only for the equation...
I am just a first year student, and have not yet tackled about quadratic equations so i am not so confident with my answer.
But hope that helps as a basis.

Answer 3

You state that only two sides of the square increase, so the new area is a rectangle. (two opposite sides increase by 5 and other two opposite sides remain the same.)
The original field is a square with all sides = x and A= x^2
The new field has dimensios of x(x+5)= x^2+5x
Thus x^2 +5x - x^2= 245
5x=245
x = 49
A original = 49^2 = 2401 ft^2

Answer 4

let the original side = x ft
so new side = x+5 ft
new area = (x + 5)^2
change in area = (x+5)^2 - (x)^2 = 245
=10x + 25 = 245
ie 10x = 220
ie x = 22 ft
so original area = 484 sqft

Answer 5

Because we increase only two of the square field's sides, its area becomes:

let "a" the length of a side, A1 the original area, A2 the new area

a*(a+5) = A2
a^2 = A1

so

A2 / A1 = [ a * (a+5) ] / ( a^2 ) => A2 / A1 = (a+5) / a
=> A1 = ( A2 * a ) / ( a+5 )

I think

Answer 6

484 sq ft