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LekaFEV [45]
3 years ago
6

If the diagonal of a square is approximately 12.73, what is the length of its sides?

Mathematics
1 answer:
Alja [10]3 years ago
7 0

Answer:

The length of the sides of the square is 9.0015

Step-by-step explanation:

Given

The diagonal of a square = 12.73

Required

The length of its side

Let the length and the diagonal of the square be represented by L and D, respectively.

So that

D = 12.73

The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:

D^{2} = L^{2} + L^{2}

Solving further, we have

D^{2} = 2L^{2}

Divide both sides by 2

\frac{D^{2}}{2} = \frac{2L^{2}}{2}

\frac{D^{2}}{2} = L^2

Take Square root of both sides

\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}

\sqrt{\frac{D^{2}}{2}} = L

Reorder

L = \sqrt{\frac{D^{2}}{2}}

Now, the value of L can be calculated by substituting 12.73 for D

L = \sqrt{\frac{12.73^{2}}{2}}

L = \sqrt{\frac{162.0529}{2}}

L = \sqrt{{81.02645}

L = 9.001469325

L = 9.0015 (Approximated)

Hence, the length of the sides of the square is approximately 9.0015

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