Question

In a rhombus VENU, diagonals VN and EU intersect at S. If VN= 12 and EU=16, what is the perimeter of the rhombus?

Answer 1

40 un.

Explanation:

The diagonals of the rhombus bisect each other at right angle. This gives us that

• 
  `VS=(1)/(2)VN=6\ un.;`
• 
  `ES=(1)/(2)EU=8\ un. ;`
• 
  `\angle VSE=90^(\circ).`

By the Pythagorean theorem,

`VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.`

The sides of the rhombus are all of the same length, then the perimeter of the rhombus is

`P_(VENU)=4\cdot 10=40\ un.`