Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 12 inches, and the width QR is labeled as 6 inches. The side LM of the square is labeled as 6 inches
Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
(make it sound like an eight grade girl who wants to show her work but not a lot, also make it less than 200 words)
To determine if Sam is correct, we need to calculate the lengths of diagonal SQ and OM and compare them.
First, let's find the length of diagonal SQ in the rectangle PQRS. We can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Given that the length SR is 12 inches and the width QR is 6 inches, we can use these measurements to find the length of diagonal SQ.
Using the Pythagorean theorem:
SQ^2 = SR^2 + QR^2
SQ^2 = 12^2 + 6^2
SQ^2 = 144 + 36
SQ^2 = 180
SQ = √180
SQ ≈ 13.42 inches
Next, let's find the length of diagonal OM in the square LMNO. Both sides of the square are labeled as 6 inches, so all sides are equal.
Using the Pythagorean theorem:
OM^2 = LM^2 + LO^2
OM^2 = 6^2 + 6^2
OM^2 = 36 + 36
OM^2 = 72
OM = √72
OM ≈ 8.49 inches
Therefore, the length of diagonal SQ is approximately 13.42 inches, while the length of diagonal OM is approximately 8.49 inches.
Since the length of diagonal SQ is not two times the length of diagonal OM, Sam's statement is incorrect. The lengths of the diagonals are not proportional in this case.