The diagonal of a rectangular field is 60 metre more than the shorter side. If the longer side is 30 metre more than the shorter side, find the sides of the field.

Sub Grade: 9

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(90m,120m)

(40m,70m)

(90m,100m)

(12m,70m)

answer is A.

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Detailed Solution

Let shorter side be = x
According to Question
Larger side =(x+30)
Diagonal =(x+60)
Using pythagoras theorem
⇒(x+60)2= (x)2+(x+30) 2
⇒x2+3600+120x= x2+x2+900+60x
⇒x2-80x-2700=0
⇒x2-90x+30x-2700=0
⇒x(x-90)+30(x-90) = 0
⇒(x-90)(x+30)=0
⇒x-90=0 x=90
⇒x+30=0
⇒x=-3 (because of length not in negative )
⇒Longer side = x+30
90+30=120m
⇒Shorter side = x
=90m
⇒Side -( 90m,120m)

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