A rectangular field is L metre long and B metres wide. It's perimeter is 280 metres. If the length is two and half times it's breath, find the values of L and B
Let's assume that the width of the rectangular field is B meters.
According to the problem, the length is two and a half times its width, so the length is 2.5B meters.
The perimeter of a rectangle can be found by using the formula: perimeter = 2(length + width).
So, the perimeter of this field is 2(2.5B + B) = 2(3.5B) = 7B meters.
According to the problem, the perimeter is 280 meters, so 7B = 280.
Dividing both sides of the equation by 7, we get B = 280/7 = 40.
If the width is 40 meters, the length is 2.5B = 2.5 * 40 = 100 meters.
Therefore, the values of L and B are L = 100 meters and B = 40 meters.
Let's solve this step-by-step:
Given:
Length of the rectangular field = L
Width of the rectangular field = B
Perimeter of the rectangular field = 280 meters.
Length is two and a half times its width: L = 2.5B.
To find the values of L and B, we can start by using the formula for the perimeter of a rectangle:
Perimeter = 2(L + B)
Substituting the given perimeter into the formula, we have:
280 = 2(L + B)
Now let's substitute the given relationship between the length and width:
280 = 2(2.5B + B)
Simplifying the equation further:
280 = 2(3.5B)
280 = 7B
Divide both sides of the equation by 7 to isolate B:
B = 280/7
B = 40
Now we can substitute the value of B back into the length equation:
L = 2.5B
L = 2.5(40)
L = 100
Therefore, the length of the rectangular field (L) is 100 meters, and the width (B) is 40 meters.
To find the values of L and B, we need to set up a system of equations based on the given information.
Let's assign L as the length and B as the width of the rectangular field.
We are given two pieces of information:
1. The perimeter of the field is 280 meters. The formula for the perimeter of a rectangle is: P = 2L + 2B. So we can write this as:
2L + 2B = 280
2. The length is two and a half times the width. This can be written as:
L = 2.5B
Now we can solve the system of equations:
Start with the second equation, L = 2.5B, and substitute it into the first equation:
2(2.5B) + 2B = 280
Simplify the equation:
5B + 2B = 280
Combine like terms:
7B = 280
Divide both sides by 7:
B = 40
Now substitute the value of B back into the equation L = 2.5B:
L = 2.5(40)
L = 100
Therefore, the length (L) of the rectangular field is 100 meters and the width (B) is 40 meters.