Answer:
The length of [tex]\overline {FH}[/tex] is;
D. 38 units
Step-by-step explanation:
The given parameters are;
The type of the given quadrilateral FGHI = Rectangle
The diagonals of the quadrilateral = [tex]\overline {FH}[/tex] and [tex]\overline {GI}[/tex]
The length of IE = 3·x + 4
The length of EG = 5·x - 6
We have from segment addition postulate, [tex]\overline {GI}[/tex] = IE + EG
The properties of a rectangle includes;
1) Each diagonal bisects the other diagonal into two
Therefore, [tex]\overline {FH}[/tex] bisects [tex]\overline {GI}[/tex], into two equal parts, from which we have;
IE = EG
[tex]\overline {GI}[/tex] = IE + EG
3·x + 4 = 5·x - 6
4 + 6 = 5·x - 3·x = 2·x
10 = 2·x
∴ x = 10/2 = 5
From which we have;
IE = 3·x + 4 = 3 × 5 + 4 = 19 units
EG = 5·x - 6 = 5 × 5 - 6 = 19 units
[tex]\overline {GI}[/tex] = IE + EG = 19 + 19 = 38 units
[tex]\overline {GI}[/tex] = 38 units
2) The lengths of the two diagonals are equal. Therefore, the length of segment [tex]\overline {FH}[/tex] is equal to the length of segment [tex]\overline {GI}[/tex]
Mathematically, we have;
[tex]\overline {FH}[/tex] = [tex]\overline {GI}[/tex] = 38 units
∴ [tex]\overline {FH}[/tex] = 38 units.
