Question

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

Since $S(-6.5, -8.5)$ and $T(2.5, -8.5)$ share the same y-coordinate, subtract x-values:
$\text{Length of } ST = |2.5 - (-6.5)| = |9| = 9$

Step2: Calculate length of TU

Since $T(2.5, -8.5)$ and $U(2.5, 3.5)$ share the same x-coordinate, subtract y-values:
$\text{Length of } TU = |3.5 - (-8.5)| = |12| = 12$

Step3: Compute rectangle perimeter

Use perimeter formula $P=2(l+w)$ where $l=9, w=12$:
$P = 2(9 + 12) = 2(21) = 42$

Step4: Compare to Alberto's answer

Alberto's value (18) ≠ calculated perimeter (42).

Answer:

No, Alberto is not correct. The actual perimeter of rectangle STUV is 42 units, not 18 units.