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.

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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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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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let length of each tile be x then area will be x^2
thus according to condition (x+4)^2 would be the area of the new tiles

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Other answers:

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