Question

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

Answer 1

let digonal be x

shorter side be y

x = y + 60

x = 90

use Pythagoras and find side

Answer 2

let shorter side(b) be x

diagonal(d) = 60+x

length or longer side(l) =30+x

By pythagoras theorem:-

d^2=l^2 + b^2

(60+x)^2=(30+x)^2 + x^2

3600+x^2+120x=900+x^2+60x+x^2

x^2-60x-2700=0

x^2-(90-30)x-2700=0

x^2-90x+30x-2700=0

x(x-90)+30(x-90)=0

(x-90)(x+30)=0

x=90,-30
side cannot be negative
so , x=90

b=90m

and l=30+x

=30+90 =120m