The length of a side of a square field is 4 m. what will be the altitude of the rhombus, if the area of the
rhombus is equal to the square field and one of its diagonal is 2 m?
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Answer:
Step-by-step explanation:
Length of side of a square =4m
Area of square =(side)
2
=(4)
2
=16m
2
It is given that,
Area of square = Area of rhombus
∴ Area of rhombus =16m
2
Area of rhombus =
2
d
1
d
2
⇒ 16=
2
1
×2×d
2
⇒ d
2
=16
∴ The diagonal of rhombus =16m
Using Pythagoras theorem :
AB
2
=OA
2
+OB
2
AB
2
=8
2
+1
2
AB
2
=65
AB=
65
Since, rhombus is a parallelogram,
∴ area of parallelogram =AB×DE
⇒ 16=
65
×DE
⇒ DE=
65
16
cm.
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