1 Answer

Abhin Krishna KA · Answer 1 · 2023-08-19T20:06:37+0000

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,

$|d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_{1_{}}})^2$

Distance AB

A (3, 4) point B (8, 7)

x₁ = 3 y₁ = 4 x₂= 8 y₂=7

substitute the values into the formula;

$|AB|\text{ =}\sqrt[]{(8-3)^2+(7-4)^2}$

simplify

$|AB|=\sqrt[]{5^2+3^2}$
$=\sqrt[]{25\text{ + 9}}=\sqrt[]{34}\text{ }\approx5.83$

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

$|BC|=\sqrt[]{(0-7)^2+(5-8)^2}$
$=\sqrt[]{(-7)^2+(-3)^2}$

$=\sqrt[]{49\text{ + 9}}=\sqrt[]{58}\approx7.62$

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

$|CA|\text{ =}\sqrt[]{(3-5)^2+(4-0)^2}$
$=\sqrt[]{(-2)^2+4^2}$
$=\sqrt[]{4+16}=\sqrt[]{20}=4.47$

Perimeter = |AB| + |BC| + |CA|

=5.83 + 7.62 + 4.47

=17.92

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