Explanation:
\({\ell _1} + x = \frac{\lambda }{4} = 22.7\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
\({\ell _2} + x = \frac{{3\lambda }}{4} = 70.2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
\({\ell _3} + x = \frac{{5\lambda }}{4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 3 \right)\)
From equations (1) and (2)
\(x = \frac{{{\ell _2} - 3{\ell _1}}}{2} = \frac{{70.2 - 68.1}}{2} = 1.05\;cm\)
From equations (2) and (3) \(\dfrac{\ell_{3}+x}{\ell_{1}+x}=5\)
\({\ell _3} = 5{\ell _1} + 4x = 5 \times 22.7 + 4 \times 1.05 = 117.7\;cm\)
