Solve without using Trigonometry.
btw...solve it for a ninth grader
Answers
Given : A figure Showing Square and lines drawn inside square
To find : Side of Square = x
Solution:
lets draw Diagonal which intersect 7 cm line at M
a = length from 9 cm line to M
=> 7 -a = length from 14 cm line to M
now we got two Similar triangle
with sides 9 , a & √9² + a²
& 14 , (7 - a) & √ (14² + (7 - a)²)
=> 9/14 = a/(7 - a) = √9² + a² / √ (14² + (7 - a)²)
=> 63 - 9a = 14a
=> 23a = 63
=> a = 63/23
7 -a = 98/23
√9² + a² = √81 + (63/23)² = √46818 / 23 = 9√578 / 23
√ (14² + (7 - a)²) = √196 + (98/23)² = √113288 / 23 = 14√578 / 23
Diagonal = 9√578 / 23 + 14√578 / 23
=> Diagonal = 23√578 / 23
=> Diagonal = √578
Diagonal² = x² + x²
=> Diagonal² = 2x²
=> Diagonal = √2x
√2x =√578
=> x = √289
=> x = 17
Side of Square = 17 cm
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