Question

the diagonal of a rectangle field of 60m more than the shorter side .if the longer side is 30m more than the shorter side find side of the field

Answer 1

Let shorter side  = x mGiven that diagonal of a rectangular field is 60 metres more than the shorter sideSo diagonal will  = x + 60 mGiven that the longer side is 30 metres more than the shorter sideLonger side = x + 30  mAll angles in rectangle is always = 90 so that we can Use Pythagoras theorem

Diagonal 2  =  shorter side 2  +  longer side 2
Plug the values In this formula we get
(x+60)2 = (x)2   + (x+30)2
Now use the formula (a+b)2 =  a2 +b2 +2ab
We get
x2 +  120 x + 3600 = x2 +  x2 +  60 x +  900
subtract x`2  + 120 x  + 3600  both side we get


0 = x2  - 60 x - 2700
Factorize it now
x 2 -  90 x + 30 x – 2700  = 0
x ( x - 90 ) +  30 (x – 90 )=0
( x – 90 ) (x + 30 ) = 0
x- 90 = 0 or x + 30 = 0 
x = 90   or x  = - 30 any side of rectangle cannot negative  so shorter side  = x + 30 = 90 + 30 = 120Diagonal is  = x + 60 = 90 + 60 = 150