Question

Rectangle ABCD has vertices at A (-1, 1), B (2, 1), C (2, -5), and D (-1, -5). What is the perimeter of rectangle ABCD?

Answer 1

The perimeter of rectangle is 18 units

Solution:

The perimeter of rectangle is:

Perimeter = 2( length + width)

Rectangle ABCD has vertices at A (-1, 1), B (2, 1), C (2, -5), and D (-1, -5)

Let AB be the length

Let BC be the width

Find distance between A and B

The distance between two points is given as:

$d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

$(x_1, y_1) = (-1, 1)\\\\(x_2, y_2) = (2, 1)$

Therefore,

$d = \sqrt{(1-1)^2+(2+1)^2}\\\\d = \sqrt{3^2}\\\\d = 3$

Thus, AB = length = 3 units

Find the distance between B and C

$(x_1, y_1) = (2, 1)\\\\(x_2, y_2) = (2, -5)$

Therefore,

$d = \sqrt{(5+1)^2+(2-2)^2}\\\\d = \sqrt{36}\\\\d = 6$

Thus width = 6 units

Therefore,

Perimeter = 2(3+6) = 2(9) = 18

Thus perimeter of rectangle is 18 units

Answer 2

Answer:

17.5

Step-by-step explanation: