Question

The diagonal of rectangular field is 16 meters more than the shorter side. If the longer side is 14 metres more than the shorter side, find the sides of the field.

Answer 1

Let the shorter side be x
diagonal will be (16 +x) m
length = (14+x)
By Pythagors' theorem,
(16 +x)² = x² + (14 +x)²
⇒256 +x² +32 x = x² + 196 +x² + 28x
⇒x² -4x -60 =0 
⇒x² - 10x + 6x - 60 =0
⇒x (x-10) +6(x -10)=0
⇒x = 10 or -6
negative side is impossible
so length of smaller side = 10 m
longer side = 24 m
diagonal = 26 m

Answer 2

let shorter side be x
.'. diagonal is x+16
side 2=x+14
(x+14)²+x²=(x+16)²   by pythogras therom
x²+196+28x+x²=x²+256+32x
x² -4x -60 =0 
x² - 10x + 6x - 60 =0
 (x-10) +6(x -10)=0
x = 10 or -6
negative side is not possible
so length of smaller side = x=10 m
longer side =x+14=  24 m
diagonal = x+16=26 m