Question

graph rectangle tuvw with vertices t(-9, 5), u(0, -10), v(5, -7), and w(-4, 8). what is the perimeter of rectangle tuvw? write your answer as an integer or as a decimal rounded to the nearest tenth. perimeter = units

Explanation:

Step1: Calculate length of TU

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$T(-9,5), U(0,-10)$
$\sqrt{(0-(-9))^2+(-10-5)^2}=\sqrt{9^2+(-15)^2}=\sqrt{81+225}=\sqrt{306}=3\sqrt{34}\approx17.49$

Step2: Calculate length of UV

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$U(0,-10), V(5,-7)$
$\sqrt{(5-0)^2+(-7-(-10))^2}=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}\approx5.83$

Step3: Calculate perimeter of rectangle

Perimeter formula: $P=2(l+w)$
$P=2(3\sqrt{34}+\sqrt{34})=2\times4\sqrt{34}=8\sqrt{34}$

Answer:

$8\sqrt{34}$ or approximately 46.6 units