Question

a square has a side length of 6 inches. Which of the following is the length of its diagonal in inches

Answer 1

Answer:

8.5

Step-by-step explanation:

The Pythagorean theorem (a^2 + b^2 = c^2) can be used to solve this problem. We have a square with a side length of 6 inches. That means all of the sides will be 6 inches. That also means the base and the height are 6 inches. Let's now cut the square in half diagonally. We have a slope now, which is the hypotenuse. Let's put these values in the Pythagorean theorem and solve for the diagonal, or the  hypotenuse:

$6^{2} +6^{2} = c^{2}$

This is equivalent to:

$36 + 36 = c^{2}$

$\sqrt{72} =\sqrt{c^{2} }$

C = 8.5 (rounded)

Answer 2

The length of the diagonal in inches should be $6\sqrt 2$  inches

Calculation of the length in inches:

Since a square has a side length of 6 inches.

So here we assume c be the diagonal

And, a and b be the square sides

So,

$c^2 = a^2 + b^2\\\\c = \sqrt (a^2 + b^2)\\\\c = \sqrt (6^2 + 6^2)\\\\c = \sqrt 72\\\\c = \sqrt (36 \times 2)\\\\c = 6\sqrt 2$

Therefore, The length of the diagonal in inches should be $6\sqrt 2$  inches

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