A rectangular field has a perimeter of 442m. If the length and the width are in ratio 12:5 find the diagonal and 2 area of the rectangular field

L / W = 12 / 5 Multiply both sides by 5

5 L / W = 12 Multiply both sides by W

5 L = 12 W Divide both sides by 5

L = ( 12 / 5 ) W

L = 2.4 W

P = 2 W + 2 L =

2 ( W + L ) = 442 Divide both sides by 2

W * L = 221

W + 2.4 W = 221

3.4 W = 221 Divide both sides by 3.4

W = 221 / 3.4

W = 65 m

L = 2.4 W

L = 2.4 * 65 = 156 m

d = sqrt ( L ^ 2 + W ^ 2 )

d = sqrt ( 156 ^ 2 + 65 ^ 2 )

d = sqrt ( 24336 + 4225 )

d = sqrt ( 28561 )

d = 169 m

A = W * L = 65 * 156 = 10,140 m ^ 2

P = 2 W + 2 L =

2 ( W + L ) = 442 Divide both sides by 2

W + L = 221

To solve this problem, we need to find the values of the length and width of the rectangular field.

Let's assume that the length of the field is 12x and the width is 5x, where x is a common factor.

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

Since we are given that the perimeter is 442m, we can write the equation: 442 = 2*(12x + 5x)

Simplifying the equation, we get: 442 = 2*(17x)

Dividing both sides by 2, we have: 221 = 17x

Now, we can solve for x: x = 221/17

Calculating this, we find that x ≈ 13. The length of the field would be 12x ≈ 12 * 13 = 156m, and the width would be 5x ≈ 5 * 13 = 65m.

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

The formula for finding the length of the diagonal (d) of a rectangle with length (l) and width (w) is: d = √(l^2 + w^2)

Substituting the values, we can calculate the diagonal: d = √(156^2 + 65^2)

Using a calculator or software, we find that the diagonal is approximately 173.72m.

To find the area of the rectangular field, we can simply use the formula: Area = length * width

Calculating, we have: Area = 156m * 65m = 10,140 square meters.

Therefore, the diagonal of the rectangular field is approximately 173.72m, and the area of the field is 10,140 square meters.