207k views
3 votes
If the diagonal of a square is approximately 12.73, what is the length of its sides?

User WeezHard
by
9.1k points

1 Answer

2 votes

Answer:

The length of the sides of the square is 9.0015

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


(D^(2))/(2) = (2L^(2))/(2)


(D^(2))/(2) = L^2

Take Square root of both sides


\sqrt{(D^(2))/(2)} = √(L^2)


\sqrt{(D^(2))/(2)} = L

Reorder


L = \sqrt{(D^(2))/(2)}

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


L = \sqrt{(12.73^(2))/(2)}


L = \sqrt{(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

User Skypanther
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.