Question

What is the perimeter of ABCDE, rounded to the nearest whole number?

Answer 1

Answer:

option B -> 23 units

Step-by-step explanation:

To solve this question we need to find the length of each side, and we can do this finding the distance between the pair of points that make a side, using the formula:

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

Where the points are $(x_1, y_1)$ and $(x_2, y_2)$.

So, using the points A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1) and E = (2, -4), we have that:

$AB = \sqrt{(-4 - (-1))^{2} + (-2 - 2)^{2} } = 5$

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

$CD = \sqrt{(2 - 5)^{2} + (2 - (-1))^{2} } = 4.2426$

$DE = \sqrt{(5 - 2)^{2} + (-1 - (-4))^{2} } = 4.2426$

$EA = \sqrt{(2 - (-4))^{2} + (-4 - (-2))^{2} } = 6.3246$

So the perimeter of ABCDE is:

$P(ABCDE) = AB + BC + CD + DE + EA$

$P(ABCDE) = 5 + 3 + 4.2426 + 4.2426 + 6.3246 = 22.8098$

Rounding to nearest whole number we have:

$P(ABCDE) = 23$

So the answer is the option B.