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

Answer:

40 un.

Step-by-step explanation:

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

• $VS=\dfrac{1}{2}VN=6\ un.;$
• $ES=\dfrac{1}{2}EU=8\ un. ;$
• $\angle VSE=90^{\circ}.$

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

$P_{VENU}=4\cdot 10=40\ un.$