Question

Question 2 (Essay Worth 10 points)

(03.01 MC)

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.

Answer 1

Sam is incorrect.

Explanation:

Sam is incorrect. By using the Pythagorean theorem, we can find out what each diagonal is equal to.

Starting with diagonal SQ...

6^2 + 12^2

= 36 + 144

= 180

Square root of 180?

= 13.41

Diagonal OM...

6^2 + 6^2

= 36 + 36

= 72

Square root of 72?

= 8.48

Therefore, Sam is incorrect because 8.4 isn't half of 13.4.

Answer 2

Sam is incorrect.

Explanation:

Using Pythagorean Theorem, we can find the length of diagonal SQ as 13.4 (6^2 + 12^2 = c^2, 36 + 144 = c^2, sqrt(180) = c, c is approx 13.4). We can do the same for diagonal OM (6^2 + 6^2 = c^2, 36 + 36 = c^2, 72 = c^2, sqrt(72) = c, c is approx 8.5). Sam is therefore incorrect because 13.4 is not double of 8.5.