find the square of adjacent side of parallelogram is 130 sq. cm and length of one of its diagonal is 14 cm find the length of other diagonal
Answers
Let ABCD be the given parallelogram and its diagonals AC and BD intersect at point M.
AB^2 + AD^2 = 130cm, BD = 14cm MD = 1/1 BD
(i) [Diagonals of a parallelogram bisect each other]
= 1/2 × 14 = 7 cm In ∆ABD, seg AM is the median.
[From (i)] ∴ AB^2 + = 2AM^2 + 2MD^2 [Apollonius theorem]
∴ 130 = 2 AM^2 + 2(7)^2 ∴ 65 = AM^2 +49
[Dividing both by 2]
∴ AM^2 = 65 – 49 ∴ AM^2 = 16 [Taking square root of both sides] ∴ AM = √16 = 4cm Now, AC =2 AM [Diagonals of a parallelogram bisect each other] 2 × 4 = 8 cm
∴ The length of the other diagonal of the parallelogram is 8 cm.
Answer:
It is given that,
AB^2+AD^2=130sq.cm
BD=14cm
diagonals of a parallelogram bisect each other.
In triangle ABD, point O is the mid point of side BD.
BO=OD=1/2BD=7cm
AB^2+AD^2=2AO+2BO^2
130=2AO^2+2(7)^2
130=2AO^2+2×49
130=2AO^2+98
2AO=130-98
2AO=32
AO^2=32/2=16
AO=√16
AO=4
So,AC=2AO=8cm
hence,the length of the other diognal is 8cm