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Answers
Given : A figure Showing Square and perpendicular lines drawn inside square. 9 cm , 7 cm & 14 cm
To find : x , Side of Square
Solution:
9 cm line & 14 cm line are parallel line :
if We draw a line parallel to 7 cm line passing though right top corner & extend 14 cm line
then we will get a parallelogram / rectangle
Hence 14 + 9 = 23 cm cm
7 cm
Hypotenuse of right angle triangle so formed = √(23² + 7²)
= √529 + 49
= √578
= 17√2
Hypotenuse of right angle triangle so formed = Diagonal of square
Diagonal of Square = x√2
=> x√2 = 17√2
=> x = 17
Side x of the square = 17 cm
Another Method :
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
Diagonal = x√2
√2x =√578
=> x = √289
=> x = 17
Side of Square = 17 cm
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