Find the Fourth SideDate: 12/03/2001 at 20:48:36 From: Suzy Subject: Quadrilaterals The successive sides of a quadrilateral are 2,6,9, and x. If the diagonals of the quadrilateral are perpendicular, compute x. Date: 12/04/2001 at 08:17:15 From: Doctor Floor Subject: Re: quadrilaterals Hi, Suzy, Thanks for your question. The diagonals of the quadrilateral divide the figure into four right triangles: From the three right triangles with known hypotenuses we see that: t^2 + u^2 = 4 [1] u^2 + v^2 = 36 [2] v^2 + w^2 = 81 [3] Now, if we compute [1]-[2]+[3] we get: t^2 + u^2 - u^2 - v^2 + v^2 + w^2 = 4 - 36 + 81 t^2 + w^2 = 49 And thus we see that x must be equal to 7. If you have more questions, just write back. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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