Question

The diagonal of rhombus measure 16 cm and 30 cm. Find it's perimeter​

Answer 1

P = 68 cm

Explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

`(\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17`

Perimeter:

P = 4s = 4•17 = 68 cm