Question

what is the measure of the diagonal of the square to the nearest tenth of a millimetre? a) 18.9 mm b) 60.0 mm c) 75.0 mm d) 84.9 mm 60 mm

Explanation:

Step1: Recall Pythagorean theorem for square

In a square with side - length \(a\), if the diagonal is \(d\), by the Pythagorean theorem \(d^{2}=a^{2}+a^{2}\) (since in a square, the two sides forming the right - angle for the diagonal are equal). Given \(a = 60\) mm, then \(d^{2}=60^{2}+60^{2}\).
\[d^{2}=3600 + 3600=7200\]

Step2: Calculate the value of \(d\)

\[d=\sqrt{7200}\]
\[d = \sqrt{3600\times2}=60\sqrt{2}\approx60\times1.414 = 84.84\approx84.9\] mm

Answer:

d) 84.9 mm