Respuesta :

calculista

Answer:

The perimeter of the field is

[tex]P=40\sqrt{13}\ ft[/tex]

Step-by-step explanation:

we know that

In a rhombus all 4 sides are congruent.

The diagonals are perpendicular and bisect each other

so

A Rhombus can be divided into four congruent right triangles

Find the length side of the rhombus

Let

b ---> the length side of the rhombus

Applying the Pythagorean Theorem in one right triangle

[tex]b^2=30^2+20^2[/tex]

[tex]b^2=1,300[/tex]

[tex]b=\sqrt{1,300}\ ft[/tex]

Simplify

[tex]b=10\sqrt{13}\ ft[/tex]

Find the perimeter of the rhombus

The perimeter of the rhombus is equal to the sum of its four congruent sides

[tex]P=4b[/tex]

substitute the value of b

[tex]P=4(10\sqrt{13})=40\sqrt{13}\ ft[/tex]

The perimeter of this field is 144.22ft.

Data given;

  • length of a = 20ft
  • length of b = 30ft

The perimeter of a rhombus is equal to the sum of it's side lengths.

To find the side length of this rhombus, we would use Pythagorean's theorem.

[tex]l^2 = 20^2 + 30^2\\ l^2 = 400 + 900\\ l = \sqrt{1300}\\ l = 36.055ft[/tex]

Perimeter of a Rhombus

The perimeter of this rhombus would be calculated as 4 times the sum of it's side length.

[tex]P = 4L[/tex]

substitute the value of L and solve

[tex]p = 4 * 36.055\\ p = 144.22ft[/tex]

The perimeter of this rhombus is calculated as 144.22ft.

learn more on perimeter of a rhombus here;

https://brainly.com/question/11801642

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