AaronAndyson
  • AaronAndyson
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.
Mathematics
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SOLVED
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katieb
  • katieb
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AaronAndyson
  • AaronAndyson
@Michele_Laino
anonymous
  • anonymous
let length of each tile be x then area will be x^2
anonymous
  • anonymous
thus according to condition (x+4)^2 would be the area of the new tiles

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More answers

anonymous
  • anonymous
u there
anonymous
  • anonymous
*sighs * i am framing the equation u do the calculation
anonymous
  • anonymous
just solve 150x^2 = 54(x+4)^2
AaronAndyson
  • AaronAndyson
54(x+4)^2
AaronAndyson
  • AaronAndyson
How to solve?
anonymous
  • anonymous
x = 6 https://www.wolframalpha.com/input/?i=150x%5E2+%3D+54%28x%2B4%29%5E2
AaronAndyson
  • AaronAndyson
Can you explain how?
Jhannybean
  • Jhannybean
|dw:1437212473800:dw|
Jhannybean
  • Jhannybean
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.
Jhannybean
  • Jhannybean
\[\# \cdot A = \#_2 \cdot A_2\]\[150x^2= 54(x+4)^2\] Now we can easily solve for x, which is the side length of one of the tiles.
Jhannybean
  • Jhannybean
Hope that makes things clearer.
AaronAndyson
  • AaronAndyson
WHat to do to RHS?
AaronAndyson
  • AaronAndyson
@Michele_Laino
phi
  • 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
phi
  • phi
you do this \[\sqrt{ \frac{5^2}{3^2} x^2} = \sqrt{(x+4)^2} \]
phi
  • 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 \[ \frac{2x}{3}= 4\]
phi
  • 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

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