Question

Point t bisects line uv. Find uv if ut=2 7/8

Answer 1

`|SM|= (1)/(2) |SU|\\\\\Rightarrow\ \ \ (1)/(4) |SU|=x+15\ \ \ and\ \ \ (3)/(4) |SU|=4x-45\\\\|SU|=4(x+15)\ \ \ and\ \ \ |SU|= (4)/(3) (4x-45)\\\\4(x+15)=(4)/(3) (4x-45)\ /\cdot (3)/(4) \\\\3(x+15)=4x-45\\3x+45=4x-45\\3x-4x=-45-45\\-x=-90\\x=90\\\\|SU|=4(x+15)=4\cdot(90+15)=4\cdot105=420`

Answer 2

`If\ T\ bisects\ \overline{UV}\ then\ |UT|=|VT|\ and\ |UT|+|VT|=|UV|.\\\\|UT|=2(7)/(8)\to|VT|=2(7)/(8)\\\\|UV|=2(7)/(8)+2(7)/(8)=4(14)/(8)=4(7)/(4)=5(3)/(4)\\\\Answer:\boxedUV`