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 time the breadth. find the length and breadth of the field.
Let L = original field length and W = original field width.
2L + 2W = 140 (perimeter)
L+15 = 3(W-5)
L = 3W -15 -15 = 3W -30
2(3W -30) + 2W = 140
8W = 140 +60 = 200
W = 25
L = 45
L' = 60 (new dimensions)
W' = 20 "
Write back your own
To solve this problem, we can set up a system of equations. Let's call the length of the rectangular field L, and the breadth B.
We are given two pieces of information:
1. The perimeter of the field is 140m. The formula for the perimeter of a rectangle is P = 2L + 2B. Therefore, we can write the equation: 2L + 2B = 140.
2. If the length is increased by 15m and the breadth is decreased by 5m, the length will become 3 times the breadth. Mathematically, we can write this as: (L + 15) = 3(B - 5).
Now we have a system of two equations with two variables:
Equation 1: 2L + 2B = 140
Equation 2: L + 15 = 3(B - 5)
To find the solution, we can use the method of substitution or elimination. Let's use substitution:
From Equation 2, we can simplify: L + 15 = 3B - 15
Rearranging this equation: L = 3B - 30
Substitute the value of L in Equation 1 with 3B - 30:
2(3B - 30) + 2B = 140
6B - 60 + 2B = 140
8B - 60 = 140
8B = 140 + 60
8B = 200
B = 200/8
B = 25
Now substitute the value of B into Equation 2 to solve for L:
L + 15 = 3(25 - 5)
L + 15 = 3(20)
L + 15 = 60
L = 60 - 15
L = 45
Therefore, the length of the rectangular field is 45m and the breadth is 25m.