Question

1. on a math test, the students are asked to find the perimeter of rectangle stuv with vertices s(-6.5, -8.5), t(2.5, -8.5), u(2.5, 3.5), and v(-6.5, 3.5). alberto writes that the perimeter of the rectangle is 18 units. is he correct? explain.

Explanation:

Step1: Calculate length of ST

Use distance formula: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
$ST = \sqrt{(2.5 - (-6.5))^2 + (-8.5 - (-8.5))^2} = \sqrt{(9)^2 + 0} = 9$

Step2: Calculate length of TU

$TU = \sqrt{(2.5 - 2.5)^2 + (3.5 - (-8.5))^2} = \sqrt{0 + (12)^2} = 12$

Step3: Find perimeter of rectangle

Perimeter = $2(l + w) = 2(9 + 12) = 42$

Step4: Check Alberto's answer

Alberto wrote 18, which is wrong. Correct perimeter is 42.

Answer:

No, 18 units is not correct. The correct perimeter is 42 units. Alberto likely found only one side length or miscalculated the distance between vertices.