In the given diagram, the length of diagonal IE is 30. The correct option is (2) 30
From the question, we are to determine the length of diagonal IE
From the given information,
/TG/ = 16
∴ /RG/ = 16÷2 = 8
NOTE: The diagonals of a rhombus bisect each other at right angles
Then,
/GE/² = /ER/² + /RG/² (Pythagoras' theorem)
From the given information, the perimeter of the rhombus is 68
Since all the sides of a rhombus are equal to one another,
Then,
/GE/ = 68÷4
/GE/ = 17
Thus,
17² = /ER/² + 8²
289 = /ER/² + 64
/ER/² = 289 - 64
/ER/² = 225
/ER/ = √225
/ER/ = 15
But,
/IE/ = 2 × /ER/
∴ /IE/ = 30
Hence, the length of diagonal IE is 30. The correct option is (2) 30
Learn more on Calculating length of a diagonal of a rhombus here: https://brainly.com/question/12354523
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