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In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B=81, and C=225, then X = (A) 150 (B) 144 (C) 80 (D) 54 (E) 36

I solved the problem via quadratic equation: 12^2 - (15 -x)^2 = 9^2 - x^2 Is there a better way to solve the problem? Or the trick here is to quickly solve the quadratic equation?

Re: PS: three squares and a triangle [#permalink]
16 Jan 2008, 04:25

chica wrote:

Attachment:

Triangle.doc

In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B=81, and C=225, then X = (A) 150 (B) 144 (C) 80 (D) 54 (E) 36

I solved the problem via quadratic equation: 12^2 - (15 -x)^2 = 9^2 - x^2 Is there a better way to solve the problem? Or the trick here is to quickly solve the quadratic equation?

Thank you

I am not sure what is being asked but I think we should find the area of triangle, since triangle has sides 9,12,15 it is right triangle and area is height multiplied by half base * 1/2 S=12(height, because side=15 is hypotenuse)*9(base)=54 D

Re: PS: three squares and a triangle [#permalink]
16 Jan 2008, 05:49

From the figure each side of the triangle is a side of three different squares. Now given the area of square you get the side. Formula Side * Side =Area of square. So 15, 12, 9 are three ides of triangle.

Notice that the numbers fit pythogram theorem. a^2+b^2 =c^2 . So its is right angle triangle. Area of =b*h/2

Base =12, Height =9. Largest side is hypotenuse

Area =54

BTW: How did you get quadratic equation from the figure?

Re: PS: three squares and a triangle [#permalink]
16 Jan 2008, 11:14

chica wrote:

Attachment:

Triangle.doc

In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B=81, and C=225, then X = (A) 150 (B) 144 (C) 80 (D) 54 (E) 36

I solved the problem via quadratic equation: 12^2 - (15 -x)^2 = 9^2 - x^2 Is there a better way to solve the problem? Or the trick here is to quickly solve the quadratic equation?

Thank you

Im guessing your looking for the area of the triangle.

Re: PS: three squares and a triangle [#permalink]
21 Jan 2008, 07:05

Travel09 wrote:

From the figure each side of the triangle is a side of three different squares. Now given the area of square you get the side. Formula Side * Side =Area of square. So 15, 12, 9 are three ides of triangle.

Notice that the numbers fit pythogram theorem. a^2+b^2 =c^2 . So its is right angle triangle. Area of =b*h/2

Base =12, Height =9. Largest side is hypotenuse

Area =54

BTW: How did you get quadratic equation from the figure?

I got trapped by the picture even though it was not drawn to the scale.. and did not notice that the triangle - was actually right triangle . So, I draw another height.. and solved the problem that way. The equation aimed to find the new height. This is how I got the quadratic equation. It worked, unfortunately, not for GMAT when you are pressed on time..

Thanks for helping me realize my careless on this one

gmatclubot

Re: PS: three squares and a triangle
[#permalink]
21 Jan 2008, 07:05