1.

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»

Step-by-step explanation:

Given:

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

LONGER side is 14m more than the shorter side.

To find :

Lengths of the SIDES of the field.

Solution :

Let the length of the shorter side be x m.

Length of longer side = x + 14 m.

Length of diagonal = x + 16 m.

Using Pythagoras theorem :

  • x² + (x + 14)² = (x + 16)²
  • x² + 196 + x² + 28x = 256 + x² + 32
  • x² - 4x - 60 = 0
  • x² + 6x - 10x - 60 = 0
  • x(x + 6) - 10(x + 6) = 0
  • (x - 10) (x + 6) = 0
  • x = -6, 10 [x ≠ -'ve]
  • x = 10

Lengths of the sides of the field :

  • x = 10 m
  • x + 14 = 24 m

∴ The length of the sides is 10 m and 24 m.

Verification :

  • x² + (x + 14)² = (x + 16)²

⇒ (10)² + (24)² = (10 + 16)²

⇒ 100 + 576 = 26²

⇒ 676 = 676

∴ L.H.S = R.H.S

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