the diagonal of rectuangular field is 60 metres more than the shorter side. If the longer side is 30 metre
more than the shorter side, find the sides of the field.
Answers
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
Let, the shorter side of rectanglular field be x m
Then, the length of Diagonal be = (x+60) m
And Length of the longer side = (x+30) m
According to the Pythagoras theoram :
(x+60)² = (x+30)² + (x)²
=> x²+120x+3600 = x²+60x+900+x²
=> 120x +3600 = x²+60x+900
=> x²-60x-2700 = 0
=> x²+30x-90x+2700 = 0
=> x(x+30)-90(x+30) = 0
=> (x+30)(x-90) = 0
Required values of x : 90 and -30
Hence, -30 doesn't exist
So, the value of shorter side of rectanglular field will be 90 m and
Length of Diagonal and longer side will be (90+60=)150 m and (90+30=)120 m respectively.
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