EFGH is a rhombus. Given EG = 16 and FH = 12, what is the length of one side of the rhombus?

Solution:

Given EFGH is a rhombus EG = 16 and FH = 12 .

The given lines are diagonals of the rhombus

As we know that the diagonals of the rhombus perpendicularly bisect each other, the diagonals are bisected into two equal halves.

So, OE = OG = 8 and OH = OF = 6

Now consider,

triangle OEF, angle O = 90 degrees OE and OF are sides, EF is the hypotenuse

We have,

(hypotenuse)² = side² + side² 

= OE² + OF² = EF²

= 64 + 36 = 100

Hypotenuse = EF = 10

According to the property of the rhombus, all sides are equal.

Therefore, the side of the given rhombus is 10.

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EFGH is a rhombus. Given EG = 16 and FH = 12, what is the length of one side of the rhombus?

Summary:

If EFGH is a rhombus. Given EG = 16 and FH = 12, then the length of one side of the rhombus is 10 units.