Question

1. a rectangular safety flag has a height of 18 inches. the diagonals of the safety flag each measure 30 inches.

bao found the perimeter of the rectangular safety flag with the following work.
$a^{2}+b^{2}=c^{2}$
$18^{2}+b^{2}=30^{2}$
$324 + b^{2}=900$
$324 - 324 + b^{2}=900 - 324$
$b^{2}=576$
$b = \sqrt{576}$
$b = 24$
$24 + 18 = 42$, so the perimeter is 42 inches.
what mistake did bao make that caused the answer to be incorrect? write your answer in at least one complete sentence. (10 points)
show the correct work and circle the answer. (15 points)

Explanation:

Step1: Identify Bao's error

Bao incorrectly calculated the perimeter by only adding one length and one width, but a rectangle has two pairs of equal sides, so he forgot to double the sum of the length and width.

Step2: Find the rectangle's length

Use Pythagorean theorem: $a^2 + b^2 = c^2$, where $a=18$, $c=30$.
$18^2 + b^2 = 30^2$
$324 + b^2 = 900$
$b^2 = 900 - 324 = 576$
$b = \sqrt{576} = 24$

Step3: Calculate correct perimeter

Perimeter of rectangle: $2\times(\text{length}+\text{width})$
$2\times(24 + 18)$

Answer:

Mistake Explanation:

Bao's critical mistake was failing to account for all four sides of the rectangle when calculating the perimeter; he only added one length and one width instead of doubling the sum of the length and width.

Correct Perimeter:

$2\times(24 + 18) = 2\times42 = 84$ inches