#1**+1 **

Let the distance between the center of the base and the northwest corner of the base be y m

Distance between the center of the base and the west side of the base = 3/2 m = 1.5 m

Distance between the center of the base and the north side of the base = 1.5/2 m = 0.75 m

By the Pythagorean Theorem,

\((1.5)^2+(0.75)^2\ =\ y^2\\~\\ (\frac32)^2+(\frac34)^2\ =\ y^2\\~\\ \frac94+\frac{9}{16}\ =\ y^2\\~\\ \frac{45}{16}\ =\ y^2\\~\\ y^2\ =\ \frac{45}{16}\)

Again by the Pythagorean Theorem,

\(y^2+2^2\ =\ x^2\\~\\ \frac{45}{16}+4\ =\ x^2\\~\\ \frac{109}{16}\ =\ x^2\\~\\ x\ =\ \sqrt{\frac{109}{16}}\\~\\ x\ =\ \frac{\sqrt{109}}{4}\)___

hectictar Jun 2, 2019