Question

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

6 units
8 units
10 units
14 units

Answer 1

C would be the correct answer

Answer 2

(C) 10 units

Explanation:

It is given that EFGH is a rhombus and EG = 16 and FH = 12.

We know that the diagonals of the rhombus are the perpendicular bisectors, therefore OF=6, OH=6, OE=8 and OG=8.

Now, using the Pythagoras theorem in ΔOFG, we have

`(FG)^(2)=(OG)^(2)+(OF)^(2)`

`(FG)^(2)=(8)^(2)+(6)^(2)`

`(FG)^2=64+36`

`FG=√(100)`

`FG=10`

Thus, the value of the side of the rhombus will be 10 units.

Hence, option C is correct.