Question

The length of a rectangular field is 12 m and the length of its diagonal is 15 m. The area of the field is ______.

Options

• 108 m²

• 180 m²

• `30sqrt(3)` m²

• `12sqrt(15)` m²

Answer 1

The length of a rectangular field is 12 m and the length of its diagonal is 15 m. The area of the field is 108 m².

Explanation:

`l` = 12 m and diagonal (d) = 15 m.

b² = (d² – `l`²) 

= [(15)² – (12)²] m² 

= [(15 + 12)(15 – 12)] m²

= (27 × 3) m²

= 81 m²

⇒ `b = sqrt(81)` m

⇒ b = 9 m

∴ Area = (12 × 9) m²

= 108 m²