## AaronAndyson one year ago The floor of a hall is paved with 150 square tiles of a certain size.If each side of the title were 4 cm longer,it would take only 54 tiles.Find the length of each tile.

1. AaronAndyson

@Michele_Laino

2. anonymous

let length of each tile be x then area will be x^2

3. anonymous

thus according to condition (x+4)^2 would be the area of the new tiles

4. anonymous

u there

5. anonymous

*sighs * i am framing the equation u do the calculation

6. anonymous

just solve 150x^2 = 54(x+4)^2

7. AaronAndyson

54(x+4)^2

8. AaronAndyson

How to solve?

9. anonymous
10. AaronAndyson

Can you explain how?

11. anonymous

|dw:1437212473800:dw|

12. anonymous

Multiply the number of tiles by the area each tile would take. Moving on to the second portion of the question. if each side of the tile were 4 cm longer That means we're now increasing the original area of each tile by 4 units. Then we multiply the number of tiles by the new area.

13. anonymous

$\# \cdot A = \#_2 \cdot A_2$$150x^2= 54(x+4)^2$ Now we can easily solve for x, which is the side length of one of the tiles.

14. anonymous

Hope that makes things clearer.

15. AaronAndyson

WHat to do to RHS?

16. AaronAndyson

@Michele_Laino

17. phi

*** 150x^2 = 54(x+4)^2 how to solve? *** I would first divide both sides by 54 and simplify 150/54 divide top and bottom by 6 and you get 25/9 = 5^2 / 3^2 and the problem is $\frac{5^2}{3^2} x^2 = (x+4)^2$ take the square root of both sides you get $\frac{5}{3} x = x+4 \\ \frac{5}{3} x - x=4 \\ \frac{2}{3} x = 4$ and you will get x=6

18. phi

you do this $\sqrt{ \frac{5^2}{3^2} x^2} = \sqrt{(x+4)^2}$

19. phi

and gives you $\frac{5}{3} x = x+4$ to solve, add -x to both sides $\frac{5}{3} x -x = x-x+4 \\ \frac{5}{3} x - x=4$ to simplify the left side, multiply the 2nd x by 3/3 (to get a common denominator) $\frac{5x}{3} - \frac{3x}{3}=4 \\ \frac{5x-3x}{3}= 4$ 5 x's take away 3 x's leaves 2 x's $\frac{2x}{3}= 4$

20. phi

to find x, multiply both sides by 3/2, like this $\frac{3}{2} \cdot \frac{2}{3} x = \frac{3}{2} \cdot 4$ notice 3/2 * 2/3 on the left side simplifies to 1 and you get 1x or just x on the left side the right side becomes 6 x=6