SOLUTION: when each side lenth of square is increased 10 inches the resulting areas is four times as greater as it would of been if each side length had been increased by 2 inches determen t

Question 456980: when each side lenth of square is increased 10 inches the resulting areas is four times as greater as it would of been if each side length had been increased by 2 inches determen the origanl side leght of the squar

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Each side length of square is increased 10 inches, the resulting area is four times greater as it would of been, if each side length had been increased by 2 inches.
Determine the original side length of the square
:
Let s = length of original square
:
(s+10)^2 = 4(s+2)^2
FOIL
s^2 + 10s + 10s + 100 = 4(s^2 + 2s + 2s + 4)
s^2 + 20s + 100 = 4(s^2 + 4s + 4)
s^2 + 20s + 100 = 4s^2 + 16s + 16
:
Combine like terms on the left,
s^2 - 4s^2 + 20s - 16s + 100 - 16 = 0
-3s^2 + 4s + 84 = 0
:
multiply by -1, we want the coefficient of s^2 to be positive
3s^2 - 4s - 84 = 0
;
Factors to:
(3s + 14)(s - 6) = 0
the positive solution is what we want here
s = 6 inches, length of the original square
:
:
See if that's true
16^2 = 4(8^2)
256 = 4(64)

RELATED QUESTIONS
When the length of each side of a square is increased by 5 inches, the area of the... (answered by edjones)

when the length of each side of a square is increased by 5 cm, the area of the resulting... (answered by cleomenius)

Comparing Areas Suppose you have two squares, one of which is larger than the other.... (answered by josgarithmetic)

1.the classroom is 20 feet long and 30 feet wide.the principal decided that the tiles... (answered by mananth)

If one side of a square is increased by 4 inches and an adjacent side is multiplied by... (answered by Cromlix)

How do I find the length of the sides of the original square? If each side of a square... (answered by Earlsdon)

the sum of the areas of two squares is 234 square inches. Each side of the larger square... (answered by mananth)

Each side of a square is increased 5 inches. When this happens, the area is multiplied by (answered by richwmiller)

Each side of a square is increased 6 inches. When this happens, the area is multiplied by (answered by macston)