Answer:
EH = 9.4
Step-by-step explanation:
A rhombus is a quadrilateral with equal length of sides.
Given that, EF = 13 and DF = 18
⇒ DH = HF = [tex]\frac{18}{2}[/tex]
= 9
The property that the diagonals of a rhombus are at right angle to each other.
Thus, applying the Pythagoras theorem, we have;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex](EF)^{2}[/tex] = [tex](EH)^{2}[/tex] + [tex](HF)^{2}[/tex]
[tex](13)^{2}[/tex] = [tex](EH)^{2}[/tex] + [tex](9)^{2}[/tex]
169 = [tex](EH)^{2}[/tex] + 81
[tex](EH)^{2}[/tex] = 169 - 81
= 88
EH = [tex]\sqrt{88}[/tex]
= 9.381
The length EH is 9.4
