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.

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

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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step-by-step explanation: