Question

The lengths of the diagonals of a rhombus are 2x and 10x. What expression gives the perimeter of the rhombus?

Answer 1

Answer:

$P=4x\sqrt{26}\ units$

Step-by-step explanation:

we know that

The sides of a rhombus are all congruent and the diagonals are perpendicular bisectors of each other

so

Applying the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the length side of the rhombus      

a and b are the semi-diagonals

we have

$a=2x/2=x\ units\\b=10x/2=5x\ units$

substitute the values

$c^2=x^2+(5x)^2$

$c^2=26x^2$

$c=x\sqrt{26}\ units$

To find out the perimeter of the rhombus multiply the length side by 4

$P=(4)(x\sqrt{26})$

$P=4x\sqrt{26}\ units$