Question

Find the approximate perimeter of △ABC plotted below.

Answer 1

Answer: 20.0

Step-by-step explanation: Khan Academy

Answer 2

The perimeter of triangle ΔABC is approximately;

(A) 20.0

Explanation:

In ΔABC, the coordinates of the vertices are given as follows;

A(-4, 1), B(-2, 3), C(3, -4)

The length, 'l', of the sides of the triangle with known 'x', am]nd 'y' coordinates are given as follows;

`l = \sqrt{\left (y_(2)-y_(1) \right )^(2)+\left (x_(2)-x_(1) \right )^(2)}`

Therefore, we have;

The length of segment
`\overline {AB}` = √((3 - 1)² + (-2 - (-4))²) = 2·√2 ≈ 2.83

The length of segment
`\overline {BC}` = √(((-4) - 3)² + (3 - (-2))²) = √74 ≈ 8.6

The length of segment
`\overline {AC}` = √(((-4) - 1)² + (3 - (-4))²) = √74 ≈ 8.6

The perimeter of a geometric shape is equal to the sum of the length of sides of the figure

The perimeter of triangle ΔABC = (The length of segment
`\overline {AB}`) + (The length of segment
`\overline {BC}` ) + (The length of segment
`\overline {AC}`)

∴ The perimeter of triangle ΔABC = 2·√2 + √74 + √74 ≈ 20.0.