Question

13. Find the diagonal of a square if the lengths of its sides are each 16 mm. Round to the nearest tenth.

A. 16.0 mm
B. 45.3 mm
C. 22.6 mm
D. 32.0 mm​

Answer 1

`C.\ 22.6mm`

Explanation:

When one draws a diagonal in a square (a line connecting opposite corners), the halves of the square form (45-45-90) triangles. This means that the triangle follows the following ratio,

`(a)-(a)-(a√(2))`

Where (a) represents the legs or the sides adjacent to the right angle (angle with the box around it) and (
`a√(2)`) represents the hypotenuse or side opposite to the right angle.

Both legs have a length of (16)mm this is because all sides of a square are congruent, and the two sides adjacent to the right angle are both the sides of a square. One of them has the measure of (16) thus the other must have a measure of (16). This means that the diameter has the following value,

`16\sqrt2}`

In numerical form,

`\approx22.62`