# 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.

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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**

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

.'. 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