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

Answer 1

question :-

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

solution of the questions :-

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