Find the area of the adjoining parallelogram and hence find the value of x.
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Step-by-step explanation:
Given
LM = 20 cm
NQ = 10 cm
MP = 8 cm
OQ = ?
In parallelogram, opposite sides are equal
but diagonals are not equal
ON = 20 cm
ON = OP + PN
ON = 10 + 10
so
OP = 10 cm
PN = 10 cm
In a ∆mpn
mn² = mp² + pn²
(10+mq)² = 10² + 8²
100+mq² = 100 + 64
100+mq² = 164
mq² = 164 - 100
mq² = 64
mq = √64
mq = 8
MN = 10 + 8
MN = 18 cm
similarly
LO = 18 cm
In ∆OQN
on² = qn² + qo²
20² = 10² + x²
400 = 100 + x²
400 - 100 = x²
300 = x²
x = √300
x = 17.32
I hope this will help you
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