Mathematics: In the diagram below, we have $st = 2tr$ and $pq = sr = 20$. find the length $uv$.

16- 2(2w+1) = 8w - 2(8+w)16-4w-2 = 8w- 16 -2w+2 +218-4w= 8w-14-2w+4w +4w18= 12w-14+2w+14 +1432= 12w+2w-2w -2w32=10w/10= 3.2...

In the diagram below, we have $st = 2tr$ and $pq =

Ответ:

nicolesan3

15.01.2022

Mathematics

Step-by-step explanation:

1. ST=2TR and SR=20, then by segment addition postulate

$ST+TR=SR\\ \\2TR+TR=SR\\ \\3TR=20\\ \\TR=\dfrac{20}{3}\\ \\ST=2\cdot \dfrac{20}{3}=\dfrac{40}{3}$

2. Consider triangles PQU and TSU. These triangles are similar by AA similarity theorem (triangles have congruent vertical angles PUQ and TUS and congruent alternate interior angles PQU and TSU). Similar triangles have proportional corresponding sides, so

$\dfrac{QU}{US}=\dfrac{PQ}{ST}=\dfrac{20}{\frac{40}{3}}=\dfrac{60}{40}=1.5$

QU=1.5US

3. Consider triangles QUV and QSR. These triangles are similar by AA similarity theorem. Similar triangles have proportional corresponding sides, so

$\dfrac{QU}{QS}=\dfrac{UV}{SR}\\ \\\dfrac{QU}{QU+US}=\dfrac{1.5US}{1.5US+US}=\dfrac{1.5}{2.5}=0.6$

$\dfrac{UV}{SR}=0.6\Rightarrow UV=0.6SR=0.6\cdot 20=12$

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In the diagram below, we have $st = 2tr$ and $pq = sr = 20$. find the length $uv$.

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