Answer:
The approximate perimeter of △ABC is 12.34 units
Step-by-step explanation:
we know that
The perimeter of a triangle is the sum of its three length sides
so
[tex]P=AB+BC+AC[/tex]
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
we have
A(3,4), B(−1,1)
substitute the values
[tex]d=\sqrt{(1-4)^{2}+(-1-3)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]d_A_B=5\ units[/tex]
step 2
Find the distance BC
we have
B(−1,1),C(−2,5)
substitute the values
[tex]d=\sqrt{(5-1)^{2}+(-2+1)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-1)^{2}}[/tex]
[tex]d=\sqrt{5}[/tex]
[tex]d_B_C=2.24\ units[/tex]
step 3
Find the distance AC
we have
A(3,4),C(−2,5)
substitute the values
[tex]d=\sqrt{(5-4)^{2}+(-2-3)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(-5)^{2}}[/tex]
[tex]d=\sqrt{26}[/tex]
[tex]d_A_C=5.10\ units[/tex]
step 4
Find the perimeter
[tex]P=5+2.24+5.10=12.34\ units[/tex]
