A gymnasium floor is being covered by square shock-absorbing tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles

This question is incomplete, the complete question is;

A gymnasium floor is being covered by square shock-absorbing tiles.

The old gym floor required 864 square tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles  

Length of the side of one of the new shock-absorbing tiles is 12 inches

Step-by-step explanation:

Given the data in the question;

Since both the area for old tiles and new tiles are the same;

so Area of old tiles = Area of new tiles,

given that; The old gym floor required 864 square tiles and new flooring will require only 600 tiles as new tiles are 2 inches larger in length and width than the old tiles.

Now let the length of the sides of the square tiles be x

Area of a square = length × length = x × x = x²

So, Area of Old tiles = 864 × x² = 864x²

Area of New tiles = 600( x + 2 )²

= 600( x² + 4x + 4 )

= 600x² + 2400x + 2400

Now, Area of old tiles = Area of new tiles

864x² - 600x² - 2400x - 2400 = 0

264x² - 2400x - 2400 = 0

we find x

Using; x = [-b ±√( b² - 4ac )] / 2a

x = [-( -2400) ±√( (-2400)² - (4 × 264 × -2400 )] / 2( 264 )

x = [ 2400 ±√( 5760000 + 2534400) ] / 528

x = [ 2400 ±√8294400 ] / 528

x = [ 2400 ±2880 ] / 528

x = [ 2400 - 2880 ] / 528  or  [ 2400 + 2880 ] / 528

x = [ -480 / 528 ] or  [ 5280 / 528 ]

x = [ -0.909 ] or  [ 10 ]

the length of the sides of the square tiles cannot be Negative

Hence, x = 10

Therefore, the length of a side of one of the new shock-absorbing tiles will be;

⇒ x + 2 = 10 + 2 = 12 inches

Length of the side of one of the new shock-absorbing tiles is 12 inches