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A playground is in the shape of a square. If the perimeter of the playground is 40 feet, find the diagonal distance across the park. Leave your answer in radical form

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absor201

The length of diagonal of park is √200 feet.

Step-by-step explanation:

Given,

Perimeter of square playground = 40 feet

Let,

a be the length of one side.

Perimeter = 4a

[tex]4a=40\\\\a=\frac{40}{4}\\\\a=10[/tex]

Length of one side of square is 10 feet.

A diagonal will form a right triangle, where,

Diagonal = c

a = 10

b = 10

Using pythagoras theorem

[tex]a^2+b^2=c^2\\(10)^2+(10)^2=c^2\\100+100=c^2\\200=c^2\\c^2=200[/tex]

Taking square root on both sides

[tex]\sqrt{c^2}=\sqrt{200}\\c=\sqrt{200}[/tex] feet

The length of diagonal of park is √200 feet.

Keywords: perimeter, square

Learn more about perimeter at:

  • brainly.com/question/9045597
  • brainly.com/question/8955867

#LearnwithBrainly

maxwellc21

Answer:

10√2 (Simplest Radical Form)

Step-by-step explanation:

While Absor201 got √200, it is still not in simplest radical form. If you got this question from MathNation, then 10√2

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