a rectangular field is 15m long and 10m wide the otherrectangular field having same perimetre has its sides in the ratio 4:5 find the dimension of the second field
P1 = 2L + 2W = 2*15 + 2*10 = 50 M. = P2.
W/L = 4/5. W = 0.8L.
P2 = 2W + 2L.
P2 = 2*0.8L + 2L,
50 = 1.6L + 2L, L = 13.9 M.
W = 0.8L = 0.8*13.9 = 11.1 m.
To find the dimensions of the second rectangular field, we need to first determine its perimeter, then use the given ratio to calculate the dimensions.
1. Perimeter of the first field:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (15m + 10m)
Perimeter = 2 * 25m
Perimeter = 50m
2. Ratio of the sides of the second field:
The ratio of sides is given as 4:5.
3. Let's assume the dimensions of the second field as 4x and 5x.
4. Perimeter of the second field:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (4x + 5x)
Perimeter = 2 * 9x = 18x
5. Since the perimeter of the second field is equal to 50m:
18x = 50m
6. Solving for x:
x = 50m / 18
x ≈ 2.78m (rounded to two decimal places)
7. Dimensions of the second field:
Length = 4x = 4 * 2.78m ≈ 11.11m
Width = 5x = 5 * 2.78m ≈ 13.89m
Therefore, the dimensions of the second field are approximately 11.11m by 13.89m.
To find the dimensions of the second rectangular field, we need to determine the length and width of the field based on the given information about its perimeter and the ratio of its sides.
Let's start by finding the perimeter of the first rectangular field. The formula for finding the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
For the first rectangular field, the length is given as 15m and the width is given as 10m. Substituting these values into the formula, we have:
Perimeter = 2 * (15m + 10m)
Perimeter = 2 * (25m)
Perimeter = 50m
We know that the second field also has the same perimeter.
Now, let's consider the ratio of the sides for the second field. It is given that the sides are in the ratio of 4:5. This means that one side of the rectangular field is 4 units and the other side is 5 units.
Let's assume the common ratio is "x". Therefore, the length of the second field would be 4x and the width would be 5x.
Using the formula for the perimeter of a rectangle, we can set up an equation to solve for "x":
Perimeter = 2 * (Length + Width)
50m = 2 * (4x + 5x)
50m = 2 * (9x)
50m = 18x
To find the value of "x", we divide both sides of the equation by 18:
50m / 18 = 18x / 18
2.778m = x
Now that we have the value of "x", we can calculate the dimensions of the second rectangular field:
Length of the second field = 4x = 4 * 2.778m = 11.112m
Width of the second field = 5x = 5 * 2.778m = 13.89m
Therefore, the dimensions of the second rectangular field are 11.112m (length) and 13.89m (width).