Question

The quadrilateral is a rhombus.
If EF = 13 and DF = 18, find EH to the nearest tenth.

Answer 1

EH = 9.4

Explanation:

A rhombus is a quadrilateral with equal length of sides.

Given that, EF = 13 and DF = 18

⇒ DH = HF =
`(18)/(2)`

= 9

The property that the diagonals of a rhombus are at right angle to each other.

Thus, applying the Pythagoras theorem, we have;

`/hyp/^(2)` =
`/adj1/^(2)` +
`/adj2/^(2)`

`(EF)^(2)` =
`(EH)^(2)` +
`(HF)^(2)`

`(13)^(2)` =
`(EH)^(2)` +
`(9)^(2)`

169 =
`(EH)^(2)` + 81

`(EH)^(2)` = 169 - 81

= 88

EH =
`√(88)`

= 9.381

The length EH is 9.4