Question

what is the perimeter of rectangle efgh? o $sqrt{10}+sqrt{29}$ units o $2sqrt{10}+2sqrt{29}$ units o 22 units o 39 units

Explanation:

Step1: Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

For side $EF$ with $E(1,-1)$ and $F(-4,1)$:
$d_{EF}=\sqrt{(-4 - 1)^2+(1+ 1)^2}=\sqrt{(-5)^2+2^2}=\sqrt{25 + 4}=\sqrt{29}$

Step2: For side $FG$ with $F(-4,1)$ and $G(-3,4)$:

$d_{FG}=\sqrt{(-3 + 4)^2+(4 - 1)^2}=\sqrt{1^2+3^2}=\sqrt{1+9}=\sqrt{10}$

Step3: Recall rectangle property

In a rectangle, opposite sides are equal. So perimeter $P = 2(d_{EF}+d_{FG})$
$P=2\sqrt{29}+2\sqrt{10}$

Answer:

B. $2\sqrt{10}+2\sqrt{29}$ units