Question

the diagonals of a rhombus measure 16cm and 30 cm . find its perimeter.

Answer 1

A rhombus has all four sides equal.
Therefore, the perimeter of a rhombus would be $A=4s$.
The diagonals intersect each other at the centre of the rhombus.
Therefore the side will be the hypotenuse of a triangle with the other two sides 16/2 and 30/2.
Apply Pythagorean Theorem.

$P= 4\sqrt{(\frac{16}2)^2+(\frac{30}2)^2} \\ \\ P= 4\sqrt{(8^2+15^2)} \\ P= 4\sqrt{64+225} \\ P= 4\sqrt{289} \\ P= 4\sqrt{17^2} \\ P= 4*17 \\ P=68$

Ans=68cm