Question

what is the perimeter of the rectangle?
a. 16 + 2√72 units
b. 16 + 2√136 units
c 16 + 2√180 units
d. 16 + 2√244 units
the length of st is 8 units.

Explanation:

Step1: Calculate the length of \( ST \)

Since it is a rectangle, \( ST = UV \) and \( SU = TV \). The formula for the distance 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 points \(S(-9,2)\) and \(T(3,-8)\), \(x_1=-9,y_1 = 2,x_2=3,y_2=-8\). Then \(ST=\sqrt{(3+9)^2+(-8 - 2)^2}=\sqrt{12^2+(-10)^2}=\sqrt{144 + 100}=\sqrt{244}\).

Step2: Calculate the perimeter of the rectangle

The perimeter of a rectangle \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Given \(w = 8\) (length of \(SV\)) and \(l=\sqrt{244}\). So \(P=2(8+\sqrt{244})=16 + 2\sqrt{244}\).

Answer:

D. \(16 + 2\sqrt{244}\) units