question_answer 1)

                Find the areas of rectangles with the following Paris of monomials as their lengths and breaths respectively.                 (p, q); (10m, 5n); \[(20{{x}^{2}},\,5{{y}^{2}});\,(4x,\,3{{x}^{2}});\,(3mn,\,4np)\].

Answer:

                (p, q) Area of the rectangle = Length \[\times \] Breadth \[=p\times q\] \[=pq\] (10m, 5n) Area of the rectangle = Length \[\times \] Breadth \[=(10\times 5)\,\times (m\times n)\] \[=50\times (mn)\] \[=50\,mn\]                 \[(20{{x}^{2}},\,5{{y}^{2}})\]                                 Area of the rectangle = Length \[\times \] Breadth \[=(4x)\times (3{{x}^{2}})\] \[=(4\times 3)\times (x\times {{x}^{2}})\] \[=12\times {{x}^{3}}=12{{x}^{3}}\]                 (3mn, 4np)                                 Area of the rectangle \[=(3mn)\times (4np)\] \[=(3\times 4)\times (mn)\times (np)\] \[=12\times m\times (n\times n)\times p\] \[=12\,m{{n}^{2}}p\].