The Ratio of Length To Breadth of a Rectangular Field is 4 : 3. If Its Diagonal is 200 m, The Area of The Field in square meters Do it With Proof
a) 18200
b) 19200
c) 18500
d) 18900
Kripaya kar waahiat answers pradaan na kre xd....
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Answers
Answer:
19200 m²
Step-by-step explanation:
Let the length of the field be '4x' and breadth of the field be '3x'.
Using Pythagoras theorem:
⇒ length² + breadth² = diagonal²
⇒ (4x)² + (3x)² = (200)²
⇒ 16x² + 9x² = 40000
⇒ 25x² = 40000
⇒ x² = 1600 ...(1)
∴ Area of field = length * breadth
= 4x * 3x
= 12 x²
= 12(1600) [from (1)]
= 19200 m²
Answer:
Given :-
- The ratio of length and breadth of a rectangular field is 4 : 3.
- The diagonal is 200 m.
To Find :-
- What is the area of field.
Formula :-
☛ Area Of Rectangle Formula :
✰ Area Of Rectangle = Length × Breadth
Solution :-
Let,
➲ Length of Rectangular Field = 4a
➲ Breadth of Rectangular Field = 3a
First, we have to find the length and breadth of a rectangular field :
According to the question by using the Pythagoras Theorem we get,
↣ (4a)² + (3a)² = (200)²
↣ (4a × 4a) + (3a × 3a) = (200 × 200)
↣ 16a² + 9a² = 40000
↣ 25a² = 40000
↣ a² = 40000/25
↣ a² = 1600
↣ a = √1600
↣ a = √40 × 40
➦ a = 40
Hence, the required length and breadth of a rectangular field are :
➢ Length Of A Rectangular Field :
➞ Length of Rectangular Field = 4a
➞ Length of Rectangular Field = 4 × 40
➡ Length of Rectangular Field = 160 m
➣ Breadth Of A Rectangular Field :
➞ Breadth Of Rectangular Field = 3a
➞ Breadth Of Rectangular Field = 3 × 40
➡ Breadth Of Rectangular Field = 120 m
Now, we have to find the area of a rectangular field :
Given :
- Length of a rectangular field = 160 m
- Breadth of a rectangular field = 120 m
According to the question by using the formula we get,
✦ Area Of Rectangle = Length × Breadth
➪ Area Of Field = 160 m × 120 m
➠ Area Of Field = 19200 m²
∴ The area of a rectangular field is 19200 m².
Hence, the correct options is option no b) 19200 m².