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 about the length of diagonal SQ being two times the length of diagonal OM, let's find the lengths of both diagonals.
In a rectangle, the lengths of the diagonals can be found using the Pythagorean theorem. Let's find the length of diagonal SQ first. We know that the length SR of the rectangle is 12 inches and the width QR is 6 inches. Using the Pythagorean theorem, we can calculate the length of SQ as follows:
SQ² = SR² + QR²
SQ² = 12² + 6²
SQ² = 144 + 36
SQ² = 180
SQ = √180
SQ ≈ 13.416 inches
Now, let's find the length of diagonal OM in the square. We are given that the side length LM of the square is 6 inches. In a square, the diagonals are equal in length. Therefore, the length of diagonal OM is also 6 inches.
Now, comparing the two lengths, we can see that diagonal SQ is not two times the length of diagonal OM. Instead, diagonal SQ is approximately 13.416 inches while diagonal OM is exactly 6 inches.
Therefore, Sam is not correct in stating that the length of diagonal SQ is two times the length of diagonal OM. The lengths of the two diagonals are not related in that way.