Question:
A farmer has a rectangular field The length of the rectangular field is 100m more than its breadth He divides it into two parts by joining the opposite vertices as he wants to cultivate Jawar in one part and Rice in the other The length of the line that divides the field is more by 200m than breadth of the rectangular field i) Is the are area of the two parts same Give reason ii) What is the length of the shortest side of the field iii)What is the ratio between length and breadth of the rectangular field
Answer:
Let the breadth be x.
Then, Length (l) = (x + 100) m and Diagonal (d) = (x + 200) m
(i)The diagonal of a rectangle divided it into two equal parts, so area of both the parts is same, also dimensions of both the triangles are same, so area will be same.
( ii )The shortest side is breadth i.e., x.
Now, to find shortest side i.e., breadth, we will use Pythagoras theorem:
(x + 200)2 = x2 + (x + 100)2
⇒ x2 + 40000 + 400 x = x2 + x2 + 10000 + 200x using (a + b)2 = a2 + b2 + 2ab
⇒ x2 + 40000 + 400 x = 2x2 + 10000 + 200x
⇒ 2x2 + 10000 + 200x - x2 - 40000 - 400 x = 0
⇒ x2 – 30000 – 200x = 0
⇒ x2 – 200 x – 30000 = 0
⇒ x2 – (300 – 100) x – 30000 = 0
⇒ x2 – 300 x + 100x – 30000 = 0
⇒ x (x – 300) + 100 (x – 300) = 0
⇒ (x – 300) (x + 100) = 0
⇒ x + 100 = 0
⇒ x = -100, which is not possible.
⇒ x – 300 = 0
⇒ x = 300 m
∴ The shortest side i.e., breadth is 300 m.
(iii) Breadth = 300 m
Length = (x + 100) m = (300 + 100) m = 400 m
Ratio of length and breadth:
=
= 
= 4 : 3
Not what you are looking for? Go ahead and submit the question, we will get back to you.
