Question

1. what is the length of segment eg?

figure 1 shows a rectangle efgd with ef = 5, and diagonals eg and fd intersecting at h. there is a mark indicating a segment of length 7 (presumably related to the rectangles sides or other segments).

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are equal and bisect each other. So $EG = DF$, and $DH = \frac{1}{2}DF$.

Step2: Calculate length of DF

Given $DH = 7$, so $DF = 2 \times DH = 2 \times 7 = 14$.

Step3: Relate DF to EG

Since $EG = DF$, $EG = 14$.

Answer:

14