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Answers
Given : A Square and three lines 14 cm , 7 cm and 9 cm
To Find : Side of Square
Solution:
Side of Square = x
join Diagonal intersecting 7 cm line in a cm and 7 - a cm
Both triangle will be be similar
as one angle is right angle and another vertically opposite angle
a/(7 - a) = 14/9
=> 9a = 98 - 14a
=> 23a = 98
=> a = 98/23
7 -a = 7 - 98/23 = 63/23
Hypotenuse = √14² + (98/23)²
another Hypotenuse = ( 9/14) √14² + (98/23)² (using similar triangle ratio)
=> Diagonal = √14² + (98/23)² + ( 9/14) √14² + (98/23)²
=> Diagonal = (1 + 9 /14)√14² + (98/23)²
=> Diagonal = (23/14)√14² + (98/23)²
=> Diagonal = √23² + 7²
=> Diagonal = √578
x√2 = √578
=> x = √289
=> x =17
Side of Square = 17 cm
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Answer:
sides of square = 17 cm is your answer.