Question

What is the perimeter, in units, of ΔABC

Δ
A
B
C
with A(−1,−6)
A
(
−
1
,
−
6
)
, B(7,−6)
B
(
7
,
−
6
)
, and C(3,−3)
C
(
3
,
−
3
)
?

Answer 1

To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).

Applying this formula, we can find the lengths of the sides of the triangle as follows:

AB = sqrt((7 - (-1))^2 + (-6 - (-6))^2) = sqrt(8^2 + 0^2) = sqrt(64) = 8

BC = sqrt((3 - 7)^2 + (-3 - (-6))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

AC = sqrt((-1 - 3)^2 + (-6 - (-3))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

Thus, the perimeter of triangle ABC is 8 + 5 + 5 = 18 units.