Question

what is the perimeter of square abcd? o $sqrt{37}$ units o $4sqrt{37}$ units o 28 units o 37 units d(-3,5) a(3,4) c(-4,-1) b(2,-2)

Explanation:

Step1: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For side AB with $A(3,4)$ and $B(2,-2)$, we have $x_1 = 3,y_1 = 4,x_2=2,y_2=-2$.
$d_{AB}=\sqrt{(2 - 3)^2+(-2 - 4)^2}=\sqrt{(-1)^2+(-6)^2}=\sqrt{1 + 36}=\sqrt{37}$.

Step2: Calculate perimeter of square

Since it is a square, all sides are equal. The perimeter $P$ of a square with side - length $s$ is $P = 4s$. Here $s=\sqrt{37}$, so $P = 4\sqrt{37}$.

Answer:

$4\sqrt{37}$ units