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Asked by Abhishek Last Modified
Answer 
Let the length of the shorter side be x metres.
The length of the diagonal= 60+x metres
The length of the longer side =30+x metres
Applying Pythagoras theorem,
Diagonal²=longer side²+shorter side²
(60+x) ²= (30+x) ² + x²
3600+120x+x²=900+60x+x²+x²
2700+60x-x²=0
2700+90x-30x-x²=0
90(30+x)-x(30+x) =0
X=90,
Shorter side is 90m, longer side is 90+30=120m
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(x+30)+x
= (x+60)
x+60x+900+x2=x2+3600+120x
x=(60120)/2
x=90
short side = 90m
long side =120m
diagonal=150m
read less
Mandeep Kaur
Computer Programming Languages Trainer (Javascript , Python etc)
Let the shorter side be x. Therefore, the diagonal = x + 60 & the longer side = x + 30.
Using the Pythagoras theorem,
x² + (x + 30)² = (x + 60)²
or x² + x² + 60x + 900 = x² + 120x + 3600
or x² - 60x - 2700 = 0
or x² - 90x + 30x - 2700 = 0
or x(x - 90) + 30(x - 90) = 0
or (x - 90) (x + 30) = 0
x = 90 or x = - 30
Since length can't be negative, therefore, the shorter side is 90m & the longer side is 120m.
read less
The longest side of the triangles i.e. the hypotenuse.
So, by Pythagoras Theorem,
(Diagonal)² = (Smaller Side)² + (Longer Side)²
(x + 60)² = (x)² + (x + 30)²
x² + 120x + 3600 = x² + x² + 60x + 900
x² + 60x - 120x + 900 - 3600 = 0
x² - 60x - 2700 = 0
x² - 90x + 30x - 2700 = 0
x(x - 90) + 30(x - 90) = 0
(x - 90) (x + 30) = 0
x = 90 because x = -30 as length cannot be possible.
So the length of the shorter side is 90 meters and the length of the longer side is 90 + 30 = 120 meters.
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