To find the perimeter
we will find the distants between the points
Let point A = (3, 4) point B = (8, 7) point C = (5, 0)
using the distance formula,
[tex]|d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_{1_{}}})^2[/tex]
Distance AB
A (3, 4) point B (8, 7)
x₁ = 3 y₁ = 4 x₂= 8 y₂=7
substitute the values into the formula;
[tex]|AB|\text{ =}\sqrt[]{(8-3)^2+(7-4)^2}[/tex]
simplify
[tex]|AB|=\sqrt[]{5^2+3^2}[/tex][tex]=\sqrt[]{25\text{ + 9}}=\sqrt[]{34}\text{ }\approx5.83[/tex]
Next. we will find the distance BC
B (8, 7) C (5, 0)
x₁ = 8 y₁ = 7 x₂= 5 y₂=0
substitute into the formula and then evaluate
[tex]|BC|=\sqrt[]{(0-7)^2+(5-8)^2}[/tex][tex]=\sqrt[]{(-7)^2+(-3)^2}[/tex]
[tex]=\sqrt[]{49\text{ + 9}}=\sqrt[]{58}\approx7.62[/tex]
we will now move to find distance CA
(5, 0) (3,4)
x₁ = 5 y₁ = 0 x₂= 3 y₂=4
substitute int the formula and then simplify
[tex]|CA|\text{ =}\sqrt[]{(3-5)^2+(4-0)^2}[/tex][tex]=\sqrt[]{(-2)^2+4^2}[/tex][tex]=\sqrt[]{4+16}=\sqrt[]{20}=4.47[/tex]
Perimeter = |AB| + |BC| + |CA|
=5.83 + 7.62 + 4.47
=17.92
