A farmer uses 140 ft. of fencing to enclose a rectangular field. if the ratio of length to width is 3:4, find the diagonal of the field.

Any help is appreciated, thank you!

perimiter=21+2w+140ft

2(3x)+2(4x)+140
6x+8x+140
14x=140
x=10
3x=30 4x=40
the rectangle is 30' by 40'. this is a 3,4,5 right angleso the diagonal is 50'

To solve this problem, we can set up a system of equations based on the given information.

Let the length of the rectangular field be represented by 3x, and the width be represented by 4x, where x is a common scaling factor.

The perimeter of a rectangle is given by the formula P = 2(length + width). Given that the farmer uses 140 ft of fencing, we can write the equation as:

2(3x + 4x) = 140

Simplifying the equation, we have:

2(7x) = 140
14x = 140
x = 140/14
x = 10

Now, we can find the length and width by substituting x back into the expressions:

Length = 3x = 3 * 10 = 30 ft
Width = 4x = 4 * 10 = 40 ft

To find the diagonal, we can use the Pythagorean theorem, where the diagonal squared is equal to the sum of the squares of the length and width:

Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 30^2 + 40^2
Diagonal^2 = 900 + 1600
Diagonal^2 = 2500

Taking the square root of both sides, we find:

Diagonal = √2500
Diagonal = 50 ft

Therefore, the diagonal of the rectangular field is 50 ft.

To find the diagonal of the rectangular field, we need to first determine the length and width of the field.

Let's assume the length of the field is 3x, and the width is 4x.

The perimeter of a rectangle is given by the formula: P = 2(length + width).

Since the farmer uses 140 ft of fencing, we can set up the equation as follows:

140 = 2(3x + 4x)

Simplifying this equation, we get:

140 = 2(7x)

Dividing both sides of the equation by 2:

70 = 7x

Now, we can solve for x by dividing both sides of the equation by 7:

x = 70/7

x = 10

So, the length of the field is 3x = 3 * 10 = 30 ft, and the width is 4x = 4 * 10 = 40 ft.

To find the diagonal of the rectangular field, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.

In this case, the length and width of the field form two sides of a right triangle, and the diagonal is the hypotenuse.

Let's label the length as a, the width as b, and the diagonal as c.

According to the Pythagorean theorem:

c² = a² + b²

c² = 30² + 40²

c² = 900 + 1600

c² = 2500

Taking the square root of both sides of the equation, we find:

c = √2500

c = 50 ft

Therefore, the diagonal of the rectangular field is 50 ft.

W = 3/4L

2L + 2(3/4L) = 140

Solve for L and then W.

Use those values in the Pythagorean theorem.

L^2 + W^2 = D^2