In ΔPQR, side PQ = 3 cm and side PR = 25 cm. What is the area of ΔPQR ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Area of }}\Delta {\text{ }}PQR \cr & = \frac{1}{2} \times QR \times PQ \cr & {\text{Given}},\,PQ = 3\,cm \cr & QR = \sqrt {{{\left( {PR} \right)}^2} - {{\left( {PQ} \right)}^2}} \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {{{\left( {25} \right)}^2} - {3^2}} \,cm \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {625 - 9} \,cm \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {616} \,cm \cr & \,\,\,\,\,\,\,\,\,\, = 2\sqrt {154} \,cm \cr & \therefore {\text{Area}}\,{\text{of}}\,\Delta \,PQR \cr & = \left( {\frac{1}{2} \times 2\sqrt {154} \times 3} \right)c{m^2} \cr & = 3\sqrt {154} {\mkern 1mu} {\mkern 1mu} c{m^2} \cr} $$