Posted by Chris on Friday, March 5, 2010 at 3:44pm.
In rhombus DEFG, if m<DEF=60, and the shorter diagonal DF has a length of 7, find the length of the side of a rhombus.

Math  Reiny, Friday, March 5, 2010 at 5:18pm
In a rhombus, the diagonals rightbisect each other.
I recognize the 306090 triangle in the diagram.
then
x/2 = 3.5/1
x = 7
(sure enough, triangle DEF is equilateral)

Math  Chris, Friday, March 5, 2010 at 5:41pm
So one side of the rhombus is equal to seven? I'm still confused as to how you got your answer...

Math  Reiny, Friday, March 5, 2010 at 6:37pm
Ok, I will use a different approach this time.
Hope you make a sketch.
Since one angle is 60º, then its opposite angle is also 60º, properties of a parallelogram.
Which means the other angle pair is 120º each, (angle D = angle F = 120)
Now look at your diagram, don't you see two equilateral triangles,
triange DEF and also triangle DGF.
So all sides in those two triangles must be equal,
since DF = 7 , the sides of the rhomubus are 7 each.

Math  Chris, Saturday, March 6, 2010 at 1:33am
I see it now,because a diagonal divides a parallelogram into two congruent triangles! Thank you!!
Answer This Question
Related Questions
 Geometry  The length of each side of a rhombus is 16. The longer diagonal has ...
 geometry  The length of the smaller of the two diagonals of a rhombus is 12 and...
 Math  The larger angles of a rhombus are twice the smaller angle of the rhombus...
 Math  the larger angles of a rhombus are twice the smaller angle of the rhombus...
 Maths  the acute angles of a rhombus are 76 degrees if the shorter diagonal is ...
 geometry  The longer diagonal of a rhombus is 2 times as long as the shorter ...
 math  Each side of a rhombus is 5 inches long and the shorter diagonal is 4 ...
 math  Your question: "The shorter diagonal of a rhombus is 50 mm long. Each of ...
 geometry  the perimeter of a rhombus is 36 inches. if the longer diagonal is 14...
 geometry  A rhombus has a diagonal with a length of 17 ft. and a side ...
More Related Questions