Question

What is the perimeter of rectangle EFGH?

Answer 1

We need to identify the perimeter of the rectangle EFGH which has points as below:
G (-3, 4)
H (2, 2)
E (1, -1)
F (-4, 1)
The distance of EF, we have it:
d² = (-4-1) ² + (1--1)² = 25 + 4 = 29
d = √29
The distance from point F to point G: 
d² = (-4--3)² + (1-4)² = 1 + 9
d = √10

Hence, we can solve for the perimeter as below:
Perimeter EFGH = 2L + 2W
Perimeter EFGH = 2(√29) + 2(√10)
Perimeter EFGH = 17.09 units

The answer is the second item in the choices or the letter B which is 2√10 + 2√29 units.

Answer 2

By definition, the perimeter of a rectangle is given by:

$P = 2w + 2l$

Where,

w: width of the rectangle

l: length of the rectangle

To find the width and length, we use the formula of distance between points:

$d = \sqrt{(x2-x1) ^ 2 + (y2-y1) ^ 2}$

For the width we have:

$w = \sqrt{(- 3 - (- 4)) ^ 2 + (4-1) ^ 2}\\w = \sqrt{10}$

For the long we have:

$l = \sqrt{(- 3-2) ^ 2 + (4-2) ^ 2}\\l =\sqrt{29}$

Then, replacing values we have:

$P = 2\sqrt{10} + 2\sqrt{29}$

Answer:

the perimeter of rectangle EFGH is:

$P = 2\sqrt{10} + 2\sqrt{29}$