Question

Can you help me please. I need to find the perimeter.

Answer 1

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