Help with Algebra!!?

Question

If the sides of a square are increased by 5 meters, the area becomes 100 square meters. Find the length of the sides of the original square.

I'm lost here. Can someone explain and help me solve this thing?

Answer 1

k.....so draw a square and label the sides "x"....now...if the sides are increased by 5...the length of the sides are "x+5"

so...

(x+5) times (x+5) = 100 squared
or
(x+5)squared = 100 squared

take the square root of either side

so

x+5 = 10
x = 10-5
x=5

the original side of the square were 5.

Answer 2

to = 100 a square's area would be 10 times 10 or 10 squared.
since this is the only possible answer the length of the sides of the original square are 5 meters.

Answer 3

if the length of the sides of the square increase by 5 meters that means the new length is 5x....and to find the area of a square it's length times width...and since a square is symetrical the equation would be (5x) times (5x) =100 so 25x^2=100 all you have to do is solve for x and that is the length of the side of the original square


and in case you can't figure that out solving 25x^2=100 gives x=2 so the length of the sides of the original square is 2 meters

Answer 4

Original length = 5 meters.

To find the area of a square you multiply 2 sides. So if the area was 100, that means that each side had to be 10. Subtract the 5 you added from that and you get 5 for each side.

Answer 5

Okay let's pick a variable for the original length of the side. Pick X.

the sides of a square are increased by 5 meters:
That's like saying X+5

the area becomes 100 square meters
which means: (X+5)^2=100.

I'm sure can solve for X right?

(X+5)(X+5)=100
X^2 + 10X + 25 = 100
X^2 + 10X - 75=0 [factor]

(X-5)(X+15)

x-5=0
X=5

x+15=0
x=-15 (this answer cannot work b/c length cannot be negative, therefore 5 is the correct answer)

Answer 6

length of the sides of the original square = x
sides of a square are increased by 5 meters = x + 5
area by increasing side = (x + 5)^2 = 100

solve it...
(x + 5)^2 = 100
x + 5 = 10
x = 5

the length of the sides of the original square is 5

Answer 7

let the side of the original square be x

(x+5) ^2= 100 sq.mt.
x^2 + 10x + 25 = 100
x^2 + 10x - 75 =0

use the formula [ -b+_ (b^2 - 4*a*c)^1/2 ] /2*a
you get two answers -15 and 5 since side cannot be negative no. it is 5 mts.

also another approach if area is 100 sq. mts side has to be 10 mts. ( take square root ) so original side will be 10 - 5 = 5 mts

Answer 8

The area of a square is Length times Width...

You know all sides of a square are equal....

So your equation would be x time x equals 100 or x squared equals 100 in order to find out the sides of the enlarged square...

once you have solved for the sides of the enlarged square you'll subtract 5 from that and have the sides of the original square

Good luck!

Answer 9

Let the increased sides be x each
The initial sides would be (x-5) each
Area of square = side x side
given area= 100 sq m
so,
100 = (x)*(x)
x ^2 = 100
x= 10

since increased side is 10 m, original sides would be 10-5=5 m each

Answer 10

five meters is the length of the original sides
(x+5)squared =100
radical sign =radical sign
x+5 =10
-5 -5
x =5