Question

Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

Answer 1

Side of the rhombus = 10cm
One diagonal, d₁ = 16cm
Let d₂ be the other diagonal of the rhombus
The diagonals of a rhombus bisect each other

∴ `("d"_1/2)^2 + ("d"_2/2)^2` = side2

`8^2 + ("d"_2/2)^2` = 100

⇒ `("d"_2/2)^2` = 100 - 64 = (6)² 

⇒ `("d"_2)/(2^2)` = 6
⇒ d₂ = 12
Thus, the other diagonal of the rhombus is of length 12cm.