Question

In a square, one diagonal is 16 cm. Find the side of the square.
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Answer 1

Answer:

By definition, the sides of a square are all equal. So the diagonal of a square forms a right triangle with two adjacent sides.

According to the Pythagorean Theorem,

d2 = s2 + s2

=> d2 = 2s2

where: d = Length of the diagonal, s = length of a side

Given, d = 16

Then (16)2 = 2s2

256/2 = s2

=> s2 = 128

=> s = √(128)

=> s = 11.3 (approximate)

So, the length of the side of the square is 11.3 cm

Answer 2

Answer:

By using the following formula,

$d = \sqrt{2} a$

$16 = \sqrt{2} a$

$a = 16 \div \sqrt{2 \: } = 11.31 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 11.3$

Hence, the side of the square is 11.3cm.