a field has a rectangular shape. the length is 10 m longer than 3 times the breadth. if the length is decreased 50m and breath is increased by 4m, the length will be twice the breadth. determine the length and breadth
L = 3B + 10
L = 2B
Substitute 3B+10 for L.
(3B+10-50) = 2B
Solve for B, then L.
Width(breadth) = W.
Length = 3w + 10.
Length = 3w+10 - 50 = 3w - 40.
Width = w + 4.
3w - 40 = 2(w + 4).
W = 48 m.
Width = w + 4 = 48 + 4 = 52 m.
Length = 2 * 52 = 104 m.
Let's define the length of the field as L and the breadth as B.
According to the given information, we can form two equations:
1) L = 3B + 10 (length is 10 meters longer than 3 times the breadth)
2) L - 50 = 2(B + 4) (if length is decreased by 50 meters and breadth is increased by 4 meters, length will be twice the breadth)
Let's solve these equations to find the values of L and B.
From equation 1, we can rewrite it as:
L - 3B = 10 (subtracting 3B from both sides)
Now, let's substitute the value of L from equation 2 into this equation:
(2B + 4) - 3B = 10
2B + 4 - 3B = 10 (removing parentheses)
Combine like terms:
-B + 4 = 10 (combining 2B and -3B)
Simplify further:
-B = 6 (subtracting 4 from both sides)
Now, we can solve for B:
B = -6 (dividing by -1 on both sides)
Since breadth cannot be negative, this solution is not valid. It means there is no solution that satisfies the given conditions.
Therefore, there is no length and breadth of the field that can satisfy both conditions simultaneously.
To solve this problem, we can start by setting up two equations based on the given information.
Let's assume the breadth of the field is "b" meters.
According to the problem, the length is 10 meters longer than 3 times the breadth, so the length can be expressed as (3b + 10) meters.
Equation 1: length = 3b + 10
Next, the problem states that if the length is decreased by 50 meters and the breadth is increased by 4 meters, the resulting length will be twice the breadth.
The new length after decreasing it by 50 meters is equal to (3b + 10) - 50 = 3b - 40.
The new breadth, after increasing it by 4 meters, is equal to (b + 4) meters.
Equation 2: new length = 2 * new breadth
=> 3b - 40 = 2 * (b + 4)
=> 3b - 40 = 2b + 8
Now, we can solve Equation 2 to find the value of "b" (breadth).
Subtract 2b from both sides:
3b - 2b - 40 = 8
b - 40 = 8
Add 40 to both sides:
b = 48
Now, substitute the value of "b" back into Equation 1 to find the length:
Length = 3b + 10
Length = 3 * 48 + 10
Length = 144 + 10
Length = 154
Therefore, the length of the field is 154 meters and the breadth is 48 meters.