construct a rhombus ABCD where diagonals AC and BD are 8 cm and 9 cm respectively.
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ABCD is rhombus. If the length of A C and B D are 8 cm and 6 cm respectively, then find the length of the sides.A. 3 cmB. 5 cmC. 6 cmD. 4 cm
Question
ABCD is rhombus. If the length of AC and BD are 8 cm and 6 cm respectively, then find the length of the sides.
A
3 cm
B
4 cm
C
5 cm
D
6 cm
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Solution
The correct option is B 5 cm
Given ABCD is a rhombus.
Hence, AB = BC = CD = DA.
Given, AC = 8 cm and BD = 6 cm.
Since, ABCD is a rhombus, the diagonals AC and BD will be perpendicular bisectors.
Hence, AE = EC = 4 cm and BE = ED = 3 cm.
Now, we know that,
∠
A
E
B
=
∠
B
E
C
=
∠
C
E
D
=
∠
D
E
A
=
90
°
So, in the triangle AEB,
A
E
=
4
c
m
,
B
E
=
3
c
m
a
n
d
∠
A
E
B
=
90
°
By Pythagoreas Theorem,
A
E
2
+
B
E
2
=
A
B
2
⇒
A
B
2
=
4
2
+
3
2
=
16
+
9
=
25
⇒
A
B
2
=
25
⇒
A
B
=
5
c
m
Hence, the sides of the rhombus are of length 5 cm.