+0  
 
+1
116
1
avatar

In the diagram below, we have ST = 2*TR + 5 and PQ = SR = 30. Find the length UV.

 

 Mar 12, 2022
 #1
avatar+13883 
+1

Find the length UV.

 

Hello Guest!

 

The length of the diagram \(\overline{QR}\)  is a.

\(\overline{ST}=2\cdot \overline{TR}+5\\ \overline{ST}+\overline{TR}=30\\ 2\cdot \overline{TR}+5+\overline{TR}=30\\ \overline{TR}=\frac{25}{3}\)

\(f(x)= -\frac{30-\frac{25}{3}}{a}\cdot x+30 =-\frac{65}{3a}\cdot x+30\\ g(x)= \frac{30}{a}\cdot x \\ f(x)=g(x)\\-\frac{65}{3a}\cdot x+30 = \frac{90}{3a}\cdot x\\ \frac{155}{3a}\cdot x=30\\ x=\frac{90a}{155}=\frac{18a}{31}\)

\(g(\frac{18a}{31})=\overline{UV}=\frac{30}{a}\cdot\frac{18a}{31}=17.42\)

 

\( The\ length\ \overline{UV}\ is\ 17.42\)

laugh  !

 Mar 13, 2022
edited by asinus  Mar 13, 2022
edited by asinus  Mar 13, 2022
edited by asinus  Mar 14, 2022

24 Online Users

avatar