If the sides of a square are lengthened by 8cm, the area becomes 289cm^2. Find the length of a side of the original square.
I do not know how to do this please help me.
let the original side of the square be x cm, then the new square will have side (x+8) cm
new area = 289
(x+8)^2 = 289
x^2 + 16x + 64 = 289
x^2 + 16x - 225 = 0
(x+25)(x-9) = 0
etc.
thanks
To find the length of a side of the original square, we need to reverse the process of lengthening the sides.
Let's assume the original length of a side of the square is "x" cm.
According to the given information, when the sides are lengthened by 8 cm, the new length becomes (x+8) cm.
The area of a square is given by the formula A = s², where A represents the area and s represents the length of a side.
Given that the area after lengthening the sides is 289 cm², we can set up the following equation:
(x + 8)² = 289
To solve this equation, we can expand and simplify:
x² + 16x + 64 = 289
Rearranging the terms:
x² + 16x + 64 - 289 = 0
x² + 16x - 225 = 0
At this point, we have a quadratic equation in standard form, which we can solve by factoring, completing the square, or using the quadratic formula. To simplify the calculations, we can factorize it:
(x + 25)(x - 9) = 0
Now we have two possible solutions: x + 25 = 0 or x - 9 = 0
Solving each equation separately:
For x + 25 = 0:
x = -25
For x - 9 = 0:
x = 9
Since length cannot be negative in this context, we discard x = -25 as an extraneous solution.
Therefore, the length of a side of the original square is 9 cm.