Question

7.

Answer 1

In the given diagram, the length of diagonal IE is 30. The correct option is (2) 30

Calculating the length of a diagonal of a Rhombus

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: brainly.com/question/12354523

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