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Length of Diagonal SQ = 15.65inches

Length of Diagonal OM = 9.9 inches

Anna is WRONG.

The length of diagonal SQ IS NOT two times the length of diagonal OM

SQ ≠ 2OM

15.65 inches ≠ 2 × 9.9 inches (19.8 inches)

Step-by-step explanation:

We are given two shapes in the above question

a) Rectangle PQRS

The length SR of the rectangle is labeled as 14 inches, and the width QR is labeled as 7 inches

When a diagonal line passes through a rectangle, it divides the rectangle into two triangles.

Hence, to solve for the Length of the diagonal of PQRS, we would be using PYTHAGORAS THEOREM.

Pythagoras Theorem states that:

c² = a² + b²

where c = length of the diagonal

a = Length of the rectangle = 14 inches

b = Width of the rectangle = 7 inches

Hence,

c² = 14² + 7²

c = √(14² + 7²)

c = 15.65 inches.

Hence , the Length of the diagonal of Rectangle PQRS = SQ = 15.65 inches

b) Square LMNO

The length LM square is labeled as 7 inches, and we know that all the sides of a square are equal to one another. Hence, the width is also 7 inches.

When a diagonal line passes through a square , it divides the square into two triangles.

Hence, to solve for the Length of the diagonal of LMNO, we would be using PYTHAGORAS THEOREM.

Pythagoras Theorem states that:

c² = a² + b²

where c = length of the diagonal

a = Length of the square = 7 inches

b = Width of the square = 7 inches

Hence,

c² = 7² + 7²

c = √(7² + 7²)

c = 9.9 inches.

Hence , the Length of the diagonal of Square LMNO = OM = 9.9 inches

From the above question, Anna says that the length of diagonal SQ is two times the length of diagonal OM

According to Anna

SQ = 2OM

SQ = 15.65

OM = 9.9 × 2 = 19.8

From the above calculation, we can see that Anna is WRONG.

The length of diagonal SQ IS NOT two times the length of diagonal OM

SQ ≠ 2OM

15.65 inches ≠ 19.8 inches