Question

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 16 inches, and the width QR is labeled as 8 inches. The side LM of the square is labeled as 8 inches.

Ada says that the length of diagonal SQ is two times the length of diagonal OM.

Is Ada 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

Ada is incorrect.

Explanation:

the length of diagonal SQ is 17.89 in, and the length of diagonal OM is 11.31 in. SQ would need to be 22.62 inches long in order to be twice as long as OM.

Answer 2

She is incorrect

Explanation:

Pythagorean theorem:

16^2+8^2

256+64=320

320 is 17.89

8^2+8^2

64+64=128

√128 is 11.31

Ada is incorrect. The length of diagonal SQ is bigger than the length of diagonal OM. But it is not two times bigger.