All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Sum Adjacent Lengths (Posted on 2007-10-21)
The two diagonals of a cyclic quadrilateral EFGH are EG and FH while
the respective lengths of its adjacent sides EF and FG are 2 and 5.

It is known that Angle EFG = 60o and the area of the quadrilateral is 4√3.

Determine the sum of the lengths GH + HE.

 See The Solution Submitted by K Sengupta Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution Comment 1 of 1
`Let e = |GH| and g = |HE|.`
`Area = 4*sqrt(3)`
`     = (1/2)|EF||FE|sin(60) + (1/2)eg*sin(180-60)`
`    or`
`  eg = 6`
`|EG| = |EF|^2 + |FG|^2 - 2|EF||FG|cos(60)`
`     = e^2 + g^2 - 2eg*cos(180-60)`
`    or`
`  19 = e^2 + g^2 + eg`
`    or`
`  25 = 19 + eg = (e+g)^2`
`    or`
`  |GH|+|HE| = 5`
`One of the two possible quadrilaterals is an`
`Isosceles Trapezoid.`
` `

 Posted by Bractals on 2007-10-21 14:02:43

 Search: Search body:
Forums (0)