Question

multiple choice 1 point 3 in rectangle fghi, diagonals fh and gi intersect at e. what is the length of fh? - ie = 3x + 4 - eg = 5x - 6 38 units 19 units 10 units 5 units clear my selection previous

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are equal and bisect each other. So \( IE = EG \) and \( FH = 2 \times IE \) (since diagonals bisect, \( FH = FI + IH \), but actually \( IE = EG \), and \( FH = 2 \times IE \) as diagonals bisect each other, so \( IE = EG \)).
Set \( 3x + 4 = 5x - 6 \).

Step2: Solve for x

Subtract \( 3x \) from both sides: \( 4 = 2x - 6 \).
Add 6 to both sides: \( 10 = 2x \).
Divide by 2: \( x = 5 \).

Step3: Find IE length

Substitute \( x = 5 \) into \( IE = 3x + 4 \): \( IE = 3(5) + 4 = 15 + 4 = 19 \).

Step4: Find FH length

Since \( FH = 2 \times IE \) (diagonals bisect each other, so \( FH = 2 \times IE \)), \( FH = 2 \times 19 = 38 \).

Answer:

38 units