Question

Me podrían ayudar con esto intente tomar una foto mejor pero no pude...por favor y gracias

Answer 1

we have the following:

1.

`\begin{gathered} AB=x,BC=4x,AC=35 \\ AC=AB+BC \\ 35=x+4x \\ 35=5x \\ x=(35)/(5)=7 \\ AB=7,BC=7\cdot4=28 \end{gathered}`

2.

`\begin{gathered} AB=5,BC=6x+1,AC=42 \\ AC=AB+BC \\ 42=5+6x+1 \\ 6x=36 \\ x=(36)/(6)=6 \\ BC=6\cdot6+1=37 \end{gathered}`

3.

`\begin{gathered} AB=x+4,BC=8x-4,AC=63 \\ AC=AB+BC \\ 63=x+4+8x-4 \\ 9x=63 \\ x=(63)/(9)=7 \\ AB=7+4=11,BC=8\cdot7-4=52,AC=63 \end{gathered}`

4.

`\begin{gathered} AB=2x+4,BC=6x+15,AC=91 \\ AC=AB+BC \\ 91=2x+4+6x+15 \\ 8x=72 \\ x=(72)/(8)=9 \\ AB=2\cdot9+4=22,BC=6\cdot9+15=69,AC=91 \end{gathered}`

5.

`\begin{gathered} AB=3x-1,BC=6x+5,AC=3x+22 \\ AC=AB+BC \\ 3x+22=3x-1+6x+5 \\ 6x=18 \\ x=(18)/(6)=3 \\ AB=3\cdot3-1=8,BC=6\cdot3+5=23,AC=3\cdot3+22=31 \end{gathered}`

6.

`\begin{gathered} AB=2x-3,BC=8x-7,AC=9x+14 \\ 9x+14=2x-3+8x-7 \\ x=24 \\ AB=2\cdot24-3=45,BC=8\cdot24-7=185,AC=9\cdot24+14=230 \\ \end{gathered}`
`\begin{gathered} AB=3x+6,BC=5x+8,AC=15x \\ AC=AB+BC \\ 15x=3x+6+5x+8 \\ 7x=14 \\ x=(14)/(7)=2 \\ AB=3\cdot2+6=12,BC=5\cdot2+8=18,AC=15\cdot2=30 \end{gathered}`