Answer:
The length of shortest side is [tex]5\ units[/tex]
Step-by-step explanation:
Let
[tex]A(-3,-2),B(1,6),C(5,3)[/tex]
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(-3,-2),B(1,6)[/tex]
substitute in the formula
[tex]AB=\sqrt{(6+2)^{2}+(1+3)^{2}}[/tex]
[tex]AB=\sqrt{(8)^{2}+(4)^{2}}[/tex]
[tex]AB=\sqrt{80}=8.94\ units[/tex]
step 2
Find the distance BC
[tex]B(1,6),C(5,3)[/tex]
substitute in the formula
[tex]BC=\sqrt{(3-6)^{2}+(5-1)^{2}}[/tex]
[tex]BC=\sqrt{(-3)^{2}+(4)^{2}}[/tex]
[tex]BC=\sqrt{25}=5\ units[/tex]
step 3
Find the distance AC
[tex]A(-3,-2),C(5,3)[/tex]
substitute in the formula
[tex]AC=\sqrt{(3+2)^{2}+(5+3)^{2}}[/tex]
[tex]AC=\sqrt{(5)^{2}+(8)^{2}}[/tex]
[tex]AC=\sqrt{89}=9.43\ units[/tex]
Compare the length sides
The length of shortest side is [tex]5\ units[/tex]
