Answer:
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
