Question

1. what is the length of segment fg? image of a triangle with right angle at f, fg perpendicular to eh, eg = 10m, gh = 11m options: 4.58, 15.20, 10.49, 3.16

Explanation:

Step1: Identify the triangle type

This is a right - angled triangle \( \triangle EFH \) with \( \angle F = 90^{\circ} \), and \( FG \) is the altitude to the hypotenuse \( EH \). We know the lengths of the two segments of the hypotenuse: \( EG = 10\space m \) and \( GH=11\space m \).

Step2: Use the geometric mean theorem

The geometric mean theorem (or altitude - on - hypotenuse theorem) states that in a right - angled triangle, the length of the altitude drawn to the hypotenuse is the geometric mean of the lengths of the two segments of the hypotenuse. That is, if \( FG \) is the altitude and \( EG \) and \( GH \) are the segments of the hypotenuse, then \( FG=\sqrt{EG\times GH} \)

Step3: Substitute the values

Substitute \( EG = 10 \) and \( GH = 11 \) into the formula: \( FG=\sqrt{10\times11}=\sqrt{110}\approx 10.49 \)

Answer:

10.49