Triangle perimeter function

Find the perimeter of triangle ABC, where point A begins the coordinate system. Point B is the intersection of the graph of the linear function f: y = - 3/4• x + 3 with the x-axis, and C is the intersection of the graph of this function with the y-axis.

Final Answer:

o =  12 cm

Step-by-step explanation:

$$\begin{gathered} A=(0,0) \\ B: \\ {y}_1=0 \\ {y}_1=-3/4\cdot x_1+3 \\ 0=-3/4\cdot x_1+3 \\ 3x_1=12 \\ {x}_1=\frac{12}{3}=4 \\ {x}_1=4 \\ B=(4,0) \\ C: \\ {x}_2=0 \\ {y}_2=-3/4\cdot x_2+3=-3/4\cdot 0+3=3 \\ C=(0,3) \\ a=|BC|;b=|AC|;c=|AB| \\ a=\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}=\sqrt{(4-0{)}^2+(0-3{)}^2}=5\text{cm} \\ b=|y_2|=|3|=3 \\ c=|x_1|=|4|=4 \\ o=a+b+c=5+3+4=12\text{cm} \end{gathered}$$

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