the area of a square is 200cmsq.what will be the lenght of its diagonals?
Answers
The two sides of the square and the diagonal form a right angle triangle.
So we can use Pythagoras Theorem to find the length of the diagonal.
Find the length of one side:
Area = Length²
Length² = 200 cm²
Length = √200
Length = 10√2 cm
Find diagonal:
a² + b² = c²
(10√2)² + (10√2)² = c²
c² = 200 + 200
c² = 400
c = √400
c = 20 cm
Answer: The diagonal is 20 cm
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ALTERNATIVE METHOD : USE FORMULA
The diagonal will form a special triangle with the sides. It is a 90º - 45º - 45º triangle.
Formula to find the hypotenuse of a 90º - 45º - 45º triangle = (side)√2
Find the length of one side:
Area = Length²
Length² = 200 cm²
Length = √200
Length = 10√2 cm
Find the diagonal:
Diagonal = (10√2) (√2) = 20 cm
Answer: The diagonal is 20 cm