Question

What is the perimeter of a parallelogram whose diagonals are 6 cm and 8 cm in length?

Answer 1

It is not possible to find the sides of a parallelogram with the measures of two diagonals only.

Explanation:

Insufficient information. It is not possible to find the sides of a parallelogram with the measures of two diagonals only. It requires at what angle the diagonals intersect to use the pythagoras theorem.

Since Rhombus is a special case of a parallelogram, we can assume ithe shape to be a Rhombus and find the sides.

`"Area of Rhombus "A_R= a^2 = (1/2) d_1 * d_2`

where 'a' is the side of the rhombus and `d_1` and `d_2` the diagonals.

We know `d_1 = 6 cm, d_2 = 8cm`

`:. a^2 = (1/2) * 6 * 8 = 24 " or " a = sqrt24 cm`

`"Perimeter of Rhombus " P_R = 4 * a = 4 * sqrt24 = 19.5959 cm`