If om = 5M, AM=12cm, then find OA
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Answer:
OA will be 12 is the answer
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Let a & b are length of diagonal then
a+b=12 ________ (1) (Given)
perimeter of diagonal =2
a
2
+b
2
______ (2) Given
8
5
=2
a
2
+b
2
4
5
=
a
2
+b
2
on squaring both sides we get
(4
5
)
2
=(
a
2
+b
2
)
2
80=a
2
+b
2
_________ (3)
using equation (1) we have
80=a
2
+(12−a)
2
80=a
2
+144+a
2
−24a
2a
2
−24a+64=0
a
2
−12a+32=0
a
2
−8a−4a+32=0
a(a−8)−4(a−8)=0
(a−4)(a−8)=0
[a=4 or a=8]
from equation (1) [b=8 or 4]
∴ length of diagonals are 4 cm and 8 cm.
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