Question

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively
$(p,q);(10m,5n);(20x^2,5y^2);(4x,3x^2);(3mn,4np)$

• A. $100x^2{y}^2;12x^3;12m{n}^{2}p$
• B. $100x^2{y}^2;12x^2;12m{n}^{2}p$
• C. $100x^{2}y;12x^3;12m{n}^{2}p$
• D. $100x^2{y}^2;12x^3;12mnp$

Answer 1

The correct option is A $100x^2{y}^2;12x^3;12m{n}^{2}p$

We know that the area of a rectangle = I $\times$ b, where I = length and b = breadth.
Therefore, the areas of rectangles with pair of monomials $(p,q),(10m,5n);(20x^2,5y^2);(4x,3x^2)$and$(3mn,4np)$as their lengths and breadths are given by $p\times q=pq$
1.$10m\times n=(10\times 5)\times (m\times n)=50mn$
2. $20x^2\times 5y^2=(20\times 5)\times (x^2\times y^2)=100x^2{y}^2$
3. $4x\times 3x^2=(4\times 3)\times (x\times x^2)$
= $12x^3$
and,
4. $3mn\times 4np=(3\times 4)\times (m\times n\times n\times p)$
= $12m{n}^{2}p$