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natulia [17]
4 years ago
10

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

Mathematics
1 answer:
True [87]4 years ago
6 0

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

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