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Serggg [28]
3 years ago
11

A square has a diagonal length of 10 ft. Draw a diagram and determine the perimeter of the square.

Mathematics
1 answer:
denpristay [2]3 years ago
5 0

The perimeter of the square is: 20\sqrt2 ft

Step-by-step explanation:

The picture is attached with the answer.

the diagonal of a square divides it into two right angled-triangles.

We can use one of the triangle to find the length of side as the diagonal will be the hypotenuse of the triangle

Let a be the side of the square, then according to Pythagoras theorem

d^2=a^2+a^2\\(10)^2 = 2a^2\\2a^2=100

Dividing both sides by 2

\frac{2a^2}{2}=\frac{100}{2}\\a^2=50

Taking Square root on both sides

\sqrt{a^2}=\sqrt{50}\\a=\sqrt{25*2}\\a=\sqrt{5^2 * 2}\\a=5\sqrt{2}\ ft

Now,

P = 4a\\P = 4 * 5\sqrt{2}\\=20\sqrt{2}\ ft

Hence,

The perimeter of the square is: 20\sqrt2 ft

Keywords: Perimeter, Pythagoras Theorem

Learn more about Square at:

  • brainly.com/question/3306327
  • brainly.com/question/3375830

#learnwithBrainly

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