the perimeter of a rectangular field is 140m. if the length is increased by 15m and the breadth is decreased by 5m, the length will become 3 times the bredth. find the length and the breadth of the field.
Is some information missing? Not enough info to answer question.
let the length be x
let the breadth be y
2x+2y=140
x+y=70
y = 70-x
new length = x+15
new breadth = y-5 = 70-x-5 = 65-x
x+15 = 3(65-x)
x+15 = 195 - 3x
4x = 180
x = 45 ---> y = 70-45 = 25
the field is 45 by 25 m
check: increased length = 45+15 = 60
decreased breadth = 25-5 = 20
is 60 equal to 3 times 20 ? Sure is!
To solve this problem, we can use the formulas for the perimeter of a rectangle and the equation given.
1. Let's assume the length of the rectangle is L and the breadth is B.
2. According to the problem, the perimeter of the rectangle is 140m. The formula for the perimeter of a rectangle is P = 2L + 2B.
So, we have the equation: 2L + 2B = 140.
3. The problem also states that if the length is increased by 15m and the breadth is decreased by 5m, the length will become 3 times the breadth. We can express this information as:
L + 15 = 3(B - 5).
4. Now we have a system of two equations:
2L + 2B = 140,
L + 15 = 3(B - 5).
To solve this system, we can use the substitution method:
5. Rearrange the second equation to solve for L:
L = 3(B - 5) - 15,
L = 3B - 30 - 15,
L = 3B - 45.
6. Substitute the value of L in the first equation with 3B - 45:
2(3B - 45) + 2B = 140,
6B - 90 + 2B = 140,
8B - 90 = 140,
8B = 140 + 90,
8B = 230.
7. Solve for B:
B = 230/8,
B = 28.75.
8. Substitute the value of B back into the equation for L:
L = 3(28.75) - 45,
L = 86.25 - 45,
L = 41.25.
Therefore, the length of the rectangular field is 41.25m and the breadth is 28.75m.