Question

1. what is the length of segment vt?

figure 1 shows a rectangle srut with diagonals st and ru intersecting at point v. the length of segment vu is 5, and the length of segment ru is 4.

Explanation:

Step1: Identify rectangle properties

In rectangle SRUT, diagonals are equal and bisect each other. So $SU = RT$, and $VT = \frac{1}{2}RT$.

Step2: Calculate diagonal length

Use Pythagorean theorem on $\triangle RUT$: $RT = \sqrt{RU^2 + UT^2}$. We know $RU=4$, $UT$ is the vertical side. Wait, given $VU=5$, and since diagonals bisect, $SU=2\times VU=10$, so $RT=SU=10$.

Step3: Find length of VT

Since $VT = \frac{1}{2}RT$, substitute $RT=10$:
$VT = \frac{1}{2} \times 10$

Answer:

5