Previously asked this question, but answer was incomplete. Need to find the diagonal that connects AC as well. That's where I get stuck. Typed response appreciated; poor eyesight. Thank you!Original Question:The perimeter of a rhombus is 64 and one of its angles measures 120°. Find the length of the diagonals. Please explain and solve. (Typed response preferred, poor eyesight. Thank you!) perimeter-4awhere a is the length of the side.64=4aa=64/4.a=16.So the length of the side is 16.Let us draw the figure of rhombus and its diagonal for the given data.D161660CА6060601612016BStep 3Since the opposite angles are equal in rhombus if ZADC = 120 thenZABC = 120.In the above figure BD is the diagonal which divides the rhombus into two trianglesA ABD and A BCD.Since the sum of all the angles in rhombus is 360 and oppsoiteangles are equalZDAB = ZDCB = xSo x + x + 120 + 120 = 3602x = 360 – 2402x = 120X = 60, therefore ZDAB = 60 and ZDCB = 60So in the A ADBZDAB = 60, ZADB = 60 and ZABD = 60So A ABD is a eqiangular triangle.equiangular triangles are equilaterla triangle .So BD = AD = AB = 16.

Answered: The perimeter of a rhombus is 64 and…

Elementary Geometry For College Students, 7e

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ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Previously asked this question, but answer was incomplete. Need to find the diagonal that connects AC as well. That's where I get stuck. Typed response appreciated; poor eyesight. Thank you!

Original Question:

The perimeter of a rhombus is 64 and one of its angles measures 120°. Find the length of the diagonals. Please explain and solve. (Typed response preferred, poor eyesight. Thank you!)

perimeter-4a
where a is the length of the side.
64=4a
a=64/4.
a=16.
So the length of the side is 16.
Let us draw the figure of rhombus and its diagonal for the given data.
D
16
16
60
C
А
60
60
60
16
120
16
B
Step 3
Since the opposite angles are equal in rhombus if ZADC = 120 then
ZABC = 120.
In the above figure BD is the diagonal which divides the rhombus in
to two triangles
A ABD and A BCD.
Since the sum of all the angles in rhombus is 360 and oppsoite
angles are equal
ZDAB = ZDCB = x
So x + x + 120 + 120 = 360
2x = 360 – 240
2x = 120
X = 60, therefore ZDAB = 60 and ZDCB = 60
So in the A ADB
ZDAB = 60, ZADB = 60 and ZABD = 60
So A ABD is a eqiangular triangle.
equiangular triangles are equilaterla triangle .
So BD = AD = AB = 16.

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