Question

If the sides of a square are the lengthened by 6cm, the area becomes 100cm^2. Find the length of a side of the original square.

The length of a side of the original square is __cm.

Answer 1

do you know how to find the length of the side of a square with area 100 ?

Answer 2

it is 4 cm.

Answer 3

let the initial lentgh be x
then the given side will be x+6
now area is 100 given\[A=(x+6)^{2}=100\]\[x ^{2}+12x+36=100\]\[x ^{2}+12x-64=0\]\[x ^{2}+16x-4x-64=0\]\[(x+16)(x-4)=0\]
hence the original side of the square is 4 cm

Answer 4

when length x, area is x^2
when length x+6, are is (x+6)^2, which is 100.
therefore, x^2+36+12x=100: there fore x=4 by solving.

Answer 5

you don't really need to expand this into a quadratic
(x+6)^2 = 100
square root both sides
x+6 = 10
x = 10-6 = 4

Answer 6

Great job, Dumbcow.

Answer 7

yes it can be done like that tooo,great job!

Answer 8

or, you could just say:
The area of the current square is A=100cm^2
If the length of a side of the current square is L
then
A=L^2
L=sqrt(A)
L=sqrt(100)=10

So the length of the side of the current square is 10cm.
But we are told that it was lengthened by 6cm
so before it was lengthened it's side length was 4cm.

Try to do some of these problems yourself, and let us know at which point you are having the difficulties. It's important to really understand this material, coz there is a lot of stuff later on that's based on it.