Question

Find the approximate perimeter of rectangle ABCD plotted below.

A(-2,6)
B(3,3)
D(-8,-4)
C(-3,-7)

Answer 1

35 units

Explanation:

Perimeter of rectangle ABCD =2(L + W)

L = AD or BC (we only need to calculate one of the two)

W = AB or DC. (we only need to calculate one of the two).

Distance between A(-2, 6) and D(-8, -4):

`AD = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`A(-2, 6) = (x_1, y_1)`

`D(-8, -4) = (x_2, y_2)`

`AD = √((-8 -(-2))^2 + (-4 - 6)^2)`

`AD = √((-6)^2 + (-10)^2)`

`AD = √(36 + 100) = √(136)`

`AD = 11.7` (nearest tenth)

Distance between A(-2, 6) and B(3, 3):

`AD = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`A(-2, 6) = (x_1, y_1)`

`B(3, 3) = (x_2, y_2)`

`AB = √((3 -(-2))^2 + (3 - 6)^2)`

`AB = √((5)^2 + (-3)^2)`

`AB = √(25 + 9) = √(34)`

`AB = 5.8` (nearest tenth)

Perimeter of rectangle ABCD =2(AD + AB)

= 2(11.7 + 5.8)

= 2(17.5)

= 35 units