11. A thin metal iron-sheet is a rhombus in shape
with each side 10 m. If one of its diaginals is
16 m, find the cost of painting its both sides
at the rate of 6 per m2
Also, find the distance between the opposite
sides of this rhombus.
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Answer:
ANSWER
In a rhombus, the diagonals bisect each other at 90
0
Let PQRS be the metal sheet.
Referring the diagram, if PR =16cm, then OP =8m, OQ =
2
SQ
Since, triangle POQ is a right angled triangle,
PQ
2
=OP
2
+OQ
2
10
2
=8
2
+(
2
SQ
)
2
(
2
SQ
)
2
=10
2
−8
2
(
2
SQ
)=
36
=6m
SQ=12m
Hence, length of the other diagonal =12m
Area of a rhombus =
2
1
×(diagonal1×diagonal2)=
2
1
×16×12=96m
2
Cost of painting both sides of the sheet =2×Area of one side×Cost per sqm=2×96×6=Rs 1152
Step-by-step explanation:
hope it helps
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