CORRECT Question

The length of a rectangular field is GREATER than twice its breadth by 10m. Its diagonal is 5m more than the length. FIND the area of the field

Answer:

The required area of the field is 1500 m²

Step-by-step explanation:

GIVEN :

• The length of a rectangular field is greater than twice its breadth by 10m.
• It's diagonal is 5m more than the length

To find :

the area of the field

Formulae :

• Area of the rectangle = length × breadth
• Diagonal of the rectangle = √(length² + breadth²)
• (a+b)² = a² + b² + 2ab

Solution :

Let

'l' be the length of the rectangle

'b' be the breadth of the rectangle

'd' be the diagonal of the rectangle

As given,

• l = 2b + 10
• d = l + 5

d = 2b + 10 + 5

d = 2b + 15

Diagonal of the rectangle is given by,

d = √(l² + b²)

Put l = 2b + 10 and d = 2b + 15,

2b + 15 = √[(2b+10)² + b²]

(2b+15)² = (2b+10)² + b²

4b² + 225 + 60b = 4b² + 100 + 40b + b²

225 - 100 + 60b - 40b = b²

125 + 20b = b²

b² – 20b – 125 = 0

By Factorization,

b² + 5b – 25b – 125 = 0

b(b + 5) – 25(b + 5) = 0

(b + 5) (b – 25) = 0

b = 25,–5

breadth can not be negative. Hence, the breadth of the rectangle is 25 m

length of the rectangle is

= 2(25) + 10

= 50 + 10

= 60 m

Area of the rectangle = length × breadth

= 60 m × 25 m

= 1500 m²