22
In a parallelogram, the lengths of the two adjacent sides are 12 cm and 14 cm respectively. If the length of one diagonal is 16 cm, find the length of the other diagonal.
- A14.6 cm
- B20.6 cm
- C18.3 cm
- D25.2 cm
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
In a parallelogram, the sum of the squares of the diagonals
= 2 × (The sum of the squares of the two adjacent sides)
= D12 + D22 = 2(a2 + b2)
Let the length of the second diagonal is ‘x’ cm.
∴ 162 + x2 = 2(122 + 142)
⇒ 256 + x2 = 2(144 + 196)
⇒ x2 = 680 – 256 = 424
⇒ x = √(424) = 20.6 cm
∴ The length of the other diagonal is 20.6 cm.
= 2 × (The sum of the squares of the two adjacent sides)
= D12 + D22 = 2(a2 + b2)
Let the length of the second diagonal is ‘x’ cm.
∴ 162 + x2 = 2(122 + 142)
⇒ 256 + x2 = 2(144 + 196)
⇒ x2 = 680 – 256 = 424
⇒ x = √(424) = 20.6 cm
∴ The length of the other diagonal is 20.6 cm.