Question

What is the perimeter of a rhombus whose diagonals are 16 and 30?

Answer 1

`68`

Explanation:

Some of the rhombus' properties:

a) The sides of a rhombus are all congruent. (the same length).
`=> AB=BC=CD=DA`

b) The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.
`=> AO=OC=1/2AC, and BO=OD=1/2BD`

Now back to our question :

Given that the two diagonals are `30, and 16`,
`=> AO=30/2=15, BO=16/2=8, angleAOB=90^@`

From Pythagorean theorem, we know
`AB^2=AO^2+BO^2`
`=> AB=sqrt(15^2+8^2)=sqrt289=17`

SInce `AB=BC=CD=DA`,
perimeter of `ABCD= 17*4=68`