Question
Let two adjacent sides of a parallelogram be a and b while the diagonals be x and y. Then x2+y2 is ___
Answer: Option A
:
A
Method 1
From the figure,
x2=BD2=(a−p)2+n2
y2=AC2=(a+p)2+n2
b2=p2+n2
∴x2+y2=2(a2+p2+n2)=2(a2+b2)
Method 2- Assumption
A rectangle is a type of parallelogram. Assume a rectangle with length = 4 and breadth = 3
Then the diagonal = 5 (Pythagoras triplet)
Thus x=y=5 and a=4 and b=3
Substitute in answer options. Only option (a) is satisfied. Hence, answer is option (a)
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:
A
Method 1
From the figure,
x2=BD2=(a−p)2+n2
y2=AC2=(a+p)2+n2
b2=p2+n2
∴x2+y2=2(a2+p2+n2)=2(a2+b2)
Method 2- Assumption
A rectangle is a type of parallelogram. Assume a rectangle with length = 4 and breadth = 3
Then the diagonal = 5 (Pythagoras triplet)
Thus x=y=5 and a=4 and b=3
Substitute in answer options. Only option (a) is satisfied. Hence, answer is option (a)
Was this answer helpful ?
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