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A square countertop has a square tile inlay in the center, [#permalink]
04 Jan 2004, 16:51

A square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. If the ration of the tiled area to the untiled area is 25 to 39, which of the following could be the width of the strip?

Let X = the side of the tiled area
Let X+2Y = the side of the countertop

We know that X^2 / [ ( X + 2Y )^2 - X^2 ] = 25 / 39
Thus, the nominator X^2 = 25 and X = 5

The denominator [ ( X + 2Y )^2 - X^2 ] = 39
X^2 + 4XY + 4Y^2 - X^2 = 39
4XY + 4Y^2 = 39
But we know that X = 5
The equation simplifies to : 4Y^2 + 20Y = 39
Plugging in 1 1/2, 3, 4 1/2, we find that only 1 1/2 satifies the equation _________________

Hey, rc197906, if you're going to post these questions, at least note that more than one answer could be correct, lest you confuse dj-- who must not remember this question from the OG-- by making him think that only one answer is correct.

think of it this way (sorry for the crude diagram - art was never my calling).

Start with 1.5

1.5 as a possible width

assume side of the square is 8 thus you have the total area of the countertop = 64

Therefore, if 1.5 is the width of the side of the tiled countertop then the side of the inlay is 5. the area of the inlay is 5x5=25. and the area of the sides are 8x8=64 minus the inlay = 39. thus we have the ratio 25/39

The other two choices are multiples of 1.5 so they will work too.

Hey, rc197906, if you're going to post these questions, at least note that more than one answer could be correct, lest you confuse dj-- who must not remember this question from the OG-- by making him think that only one answer is correct.

oohhh, yeh. each answer satisfied the solution and that made me look upside down..

think of it this way (sorry for the crude diagram - art was never my calling).

Start with 1.5

1.5 as a possible width

assume side of the square is 8 thus you have the total area of the countertop = 64

Therefore, if 1.5 is the width of the side of the tiled countertop then the side of the inlay is 5. the area of the inlay is 5x5=25. and the area of the sides are 8x8=64 minus the inlay = 39. thus we have the ratio 25/39

The other two choices are multiples of 1.5 so they will work too.

Hope this helps.

eeeeeeehhhhhhh hooooooooo..!!
TITLEIST came for my rescue

The life of a dog is good. Eat, sleep, and cuddle with beautiful women who think you're cute and cuddly. Why we were born human (especially as aspiring MBA students) beats me.

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Last edited by Titleist on 04 Jan 2004, 19:56, edited 1 time in total.