length of a rectangular field is greater than its breadth by 10m . its diagonal is 5m more than the length . find the area of the field
Answers
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