A rectangular field is 0.4m longer than it is wide if it's length is 6m ,find it's Perimeter when the breadth of the rectangle is reduced by 0.5m,the length is increased by 1/4 of its original. What is the change in the length of the rectangle.

Where is my answers

to get formula and answer

Should l add 0.4+0.4=0.8 and minus 0.5 to find the width then add the length to get the perimeter then use the perimeter+breadh to find the length then minus to find the change in length.

width = 6 - 0.4 = 5.6

so the new perimeter is
2(5.6-5 + 5/4 * 6) = 16.2 m

YES

What an answer

16.2metres

To find the formula for the perimeter of the rectangular field, we use the formula P = 2(l + b), where P is the perimeter, l is the length, and b is the width.

Given that the length is 0.4m longer than the width, and the length is 6m, we can find the width as:

b = l - 0.4
= 6 - 0.4
= 5.6m

So the original perimeter is:

P = 2(l + b)
= 2(6 + 5.6)
= 23.2m

To find the new perimeter when the width is reduced by 0.5m and the length is increased by 1/4 of the original length, we can use the same formula and substitute the new values:

New width: b - 0.5 = 5.6 - 0.5 = 5.1m
New length: l + (1/4)l = 6 + (1/4)6 = 7.5m

New perimeter:

P = 2(l + b)
= 2(7.5 + 5.1)
= 24.6m

So the change in the perimeter is:

24.6 - 23.2 = 1.4m

Therefore, the formula for the new perimeter is P = 2(7.5 + 5.1) = 24.6m, and the change in the length of the rectangle is 1.5m.

To find the perimeter of the rectangle, we need to know both the length and the width of the rectangle.

The problem states that the length of the rectangle is 6m. We also know that the length is 0.4m longer than the width. Let's call the width of the rectangle "w".

From this information, we can create an equation: length = width + 0.4m

Substituting the given length, we get: 6m = w + 0.4m

To find the width, we can rearrange the equation: w = 6m - 0.4m = 5.6m

Now we have both the length and width of the rectangle: length = 6m and width = 5.6m.

To find the original perimeter, we use the formula: Perimeter = 2 * (length + width)
Plugging in the values: Perimeter = 2 * (6m + 5.6m) = 2 * 11.6m = 23.2m

Now let's calculate the change in the length when the width is reduced by 0.5m and the length is increased by 1/4 of its original length.

The new width is 5.6m - 0.5m = 5.1m

The new length is 6m + (1/4) * 6m = 6m + 1.5m = 7.5m

The change in length is the difference between the original length and the new length: Change in length = 7.5m - 6m = 1.5m

Therefore, the change in the length of the rectangle is 1.5 meters.