Question

The diagonal of a rectangular field is 16c.m more than the shorter side .The longer side is 14 more than the shorter side.what is length of the sides and diagonal​

Answer 1

Let the shorter side be 'x'

Given :-

• Diagonal of rectangular field is 16 cm more than the shorter side
• Longer side is 14 cm more than the shorter side.

(kindly refer attachment)

To find :-

✰ Length of sides

✰ Diagonal

Method :-

Longer side ➟ (14 + x)

Diagonal ➟ (16 + x)

By applying Pythagoras theorem;

(AC)² = (AB)² + (BC)²

⇒(16 + x)² = x² + (14 + x)²

Expand using (a + b)² = a² + b² + 2ab

256 + x² + 32x = x² + 196 + x² + 28x

✒Cancelling x² on both sides,

256 + 32x = 196 + x² + 28x

⇒ 256 - 196 + 32x - 28x = x²

⇒ 60 + 4x = x²

⇒ x² - 4x - 60 = 0

Factorise x² - 4x - 60 = 0

x² + 6x - 10x - 60 = 0

⇒ x(x + 6) - 10(x + 6) = 0

⇒ (x - 10)(x + 6) = 0

Therefore,

x = 10 or -6

Side cannot be negative.

So

Shorter side = x = 10 cm

Diagonal = 16 + x = 26 cm

Longer side = 14 + x = 24 cm