Find the length of diagonal of a square whose each side measure 11 cm.
Answers
METHOD 1: By Pythagoras Theorem
a² + b² = c²
c² = 11² + 11²
c² = 121 + 121
c² = 242
c = √242
c = 11√2 cm
Answer: The diagonal is 11√2 cm
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METHOD 2: By formula
The sides and the diagonal makes a 90 - 45 - 45 right angle triangle.
Therefore the diagonal = side√2
Diagonal = 11√2 cm
Answer: The diagonal is 11√2 cm
Answer:
As you can see, a diagonal of a square divides it into two right triangles, BCD and DAB. The diagonal of the square is the hypotenuse of these triangles. We can use Pythagoras' Theorem to find the length of the diagonal if we know the side length of the square.
As a formula:
diagonal = √ s 2 + s 2
where s is the length of any side
which simplifies to:
s √ 2