In the given figure, triangle PQR is a right-angled triangle at Q. If PQ = 35 cm and QS = 28 cm, then what is the value (in cm) of SR?

Solution (By Examveda Team)

$$\eqalign{ & PQ \times QR = QS \times PR \cr & 35 \times QR = 28 \times \sqrt {{{\left( {35} \right)}^2} + Q{R^2}} \cr & {\left( {\frac{5}{4}QR} \right)^2} = {\left( {35} \right)^2} + Q{R^2} \cr & \frac{{25}}{{16}}Q{R^2} - Q{R^2} = 1225 \cr & \frac{9}{{16}}Q{R^2} = 1225 \cr & Q{R^2} = \frac{{1225 \times 16}}{9} \cr & QR = \frac{{35 \times 4}}{3} \cr & QR = \frac{{140}}{3} \cr & S{R^2} = Q{R^2} - Q{S^2} \cr & S{R^2} = {\left( {\frac{{140}}{3}} \right)^2} - {\left( {28} \right)^2} \cr & S{R^2} = \frac{{{{14}^2}\left( {{{10}^2} - 9 \times 4} \right)}}{9} \cr & S{R^2} = \frac{{{{14}^2} \times 64}}{9} \cr & SR = \frac{{14 \times 8}}{3} \cr & SR = \frac{{112}}{3} \cr & SR = 37.33{\text{ cm}} \cr} $$