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 14 inches, and the width QR is labeled as 7 inches. The side LM of the square is labeled as 7 inches.

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

Is Anna 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

Incorrect

Explanation:

Formula:

the Diagonal of a square with side square of lengths a

is equal to a√2.

=============

Then

Diagonal of LMNO : 7√2

Then

OM = 7√2

…………………………………………

Using the Pythagorean theorem:

The diagonal of the rectangle PQRS is equal to :

√(14²+7²) = √245 = 7√5

Then

SQ = 7√5

………………

Conclusion:

7√5 ≠ 2×(7√2)

Therefore

Anna is not correct.