# Math

posted by .

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 -

In a rhombus, the diagonals right-bisect each other.
I recognize the 30-60-90 triangle in the diagram.
then
x/2 = 3.5/1
x = 7
(sure enough, triangle DEF is equilateral)

• Math -

So one side of the rhombus is equal to seven? I'm still confused as to how you got your answer...

• Math -

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 -

I see it now,because a diagonal divides a parallelogram into two congruent triangles! Thank you!!

## Similar Questions

1. ### geometry

the perimeter of a rhombus is 36 inches. if the longer diagonal is 14 inches what is the length of the shorter diagonal of the rhombus?
2. ### geometry

The longer diagonal of a rhombus is 2 times as long as the shorter diagonal. Find the length of the shorter diagonal if the area is 24in squared.
3. ### math

Each side of a rhombus is 5 inches long and the shorter diagonal is 4 inches. Find the angle of the rhombus and the longer diagonal.
4. ### geometry

The length of the smaller of the two diagonals of a rhombus is 12 and the length of the larger diagonal is 16. What is the length of a side of the rhombus?
5. ### math

Your question: "The shorter diagonal of a rhombus is 50 mm long. Each of its obtuse angles measures 140. Find the length of each side."
6. ### Geometry

The length of each side of a rhombus is 16. The longer diagonal has length 26. Find the measures of the angles of the rhombus to the nearset degree.
7. ### Math

the larger angles of a rhombus are twice the smaller angle of the rhombus. if the shorter diagonal is 20, find the perimeter of the rhombus
8. ### Math

The larger angles of a rhombus are twice the smaller angle of the rhombus. If the shorter diagonal is 20, find the perimeter of the rhombus.
9. ### Maths

the acute angles of a rhombus are 76 degrees if the shorter diagonal is of length 8 cm calculate of the sides of the rhombus to the nearest mm
10. ### math

Diagonal of a rhombus are in the ratio 3:4. If its perimeter is 40cm, find the length of the side and diagonals of rhombus

More Similar Questions