Question

The side of a rhombus is 10 cm. Its one diagonal is 12 cm. Find the length of other diagonal.

Answer 1

Given: A rhombus with side s = 10 cm and one diagonal d₁ = 12 cm; find the other diagonal d₂.

Step-wise calculation:

1. Diagonals of a rhombus are perpendicular bisectors.

So, by Pythagoras on half-diagonals:

`s^2 = (d_1/2)^2 + (d_2/2)^2`

2. Substitute values:

`10^2 = (12/2)^2 + (d_2/2)^2`

⇒ `100 = 6^2 + (d_2/2)^2`

⇒ `100 = 36 + (d_2/2)^2`

⇒ `(d_2/2)^2 = 64`

⇒ `d_2/2 = 8`

⇒ d₂ = 16 cm

The other diagonal is 16 cm.