Question

find the perimeter of a square if the length of its diagonal is 16 millimeters. round to the nearest tenth.

Answer 1

Answer:

45.3 mm

Step-by-step explanation:

Use the basic 45-45-90 triangle with side length 1 as the building block here.  If the length of one side is 1, then the perimeter is 1 + 1 + 1 + 1, or 4, and the length of the diagonal is √2.

We are told that the length of the diagonal of the given square is 16 m.

Determine the length of one side of this square, using an equation of proportions:

 16        x

------ = -------

 √2       1

                                             16

Then (√2)x = 16, and x = -----------

                                             √2

The perimeter of the given square (with diagonal 16 mm)  is 4 times the side length found above, or:

      16                      16

4 ---------- = (2)(2) -----------  =  (2)(√2)(16) = 32√2 (all measurements in mm)

       √2                    √2

This perimeter, rounded to the nearest tenth, is 45.3 mm.