Question

What is the length of a diagonal of a square with a side length of 8?

A. 4
B. 42
C. 43
D. 82

Answer 1

D. 8
`√(2)`

Explanation:

To find the diagonal of the square, you can use the Pythagorean theorem* to find the hypotenuse since the diagonal cuts the square into two right triangles with legs of 8 units in length:

If in a^2 + b^2 = c^2, a = 8 and b = 8,

8^2 + 8^2 = c^2 (put 8 as both the leg lengths in the equation)

128 = c^2 (calculate 8^2 and then add the two terms together)

c = 8
`√(2)` (square both sides)

So, the length of the diagonal is 8
`√(2)` units

*the Pythagorean theorem is a theorem used to find the sides lengths of a right triangle: a^2 + b^2 = c^2. a and b are the legs of the triangle, and c is the hypotenuse.