Question

The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side then find the lengths of the sides of the field.
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Answer 1

➙ given :-

→ The diagonal of a rectangular field is 16 m more than the shorter side.

→ If the longer side is 14 m more than the shorter side

➙ To find :-

→ the length of the sides of the field

➙ Solution :-

Let the shorter side of the field be x metres.

Then, longer side = (x + 14) m.

And, diagonal = (x + 16) m.

⟹ (x + 16)² – (x + 14)² = x²

⟹ (2x + 30) × 2 = x²

⟹ x² - 4x - 60 = 0

⟹ x² - 10x + 6x - 60 = 0

⟹ x(x - 10) + 6(x - 10) = 0

⟹ (x - 10) (x+6) = 0

⟹ x-10 = 0 or x+6=0

⟹ x = 10 or x = -6

⟹ x = 10

[∵breadth cannot be negative]

therefore,breadth = 10 m and length = (10 + 14) m = 24 m.