Question

In a rectangle FGHI, diagonals FH and GI intersect at E What is the length of FH?

Answer 1

Answer:

The length of $\overline {FH}$ 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 = $\overline {FH}$ and $\overline {GI}$

The length of IE = 3·x + 4

The length of EG = 5·x - 6

We have from segment addition postulate, $\overline {GI}$ = IE + EG

The properties of a rectangle includes;

1) Each diagonal bisects the other diagonal into two

Therefore,  $\overline {FH}$ bisects $\overline {GI}$, into two equal parts, from which we have;

IE = EG

$\overline {GI}$ = 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

$\overline {GI}$ = IE + EG = 19 + 19 = 38 units

$\overline {GI}$ = 38 units

2) The lengths of the two diagonals are equal. Therefore, the length of segment $\overline {FH}$ is equal to the length of segment $\overline {GI}$

Mathematically, we have;

$\overline {FH}$ = $\overline {GI}$ = 38 units

∴ $\overline {FH}$ = 38 units.