Question

# Give possible expressions for the length and breadth of the rectangle whose area is given by(i) $$25{a^2} - 35a + 12$$(ii) $$24{x^2} - 15x$$

Solution

## (i) Let us first factorize the given expression $$25a^2-35a+12$$ as shown below:$$25a^{ 2 }-35a+12\\ =25a^{ 2 }-15a-20a+12\\ =5a(5a-3)-4(5a-3)\\ =(5a-4)(5a-3)$$Therefore, the area of the rectangle is $$(5a-4)(5a-3)$$ and we also know that the area of the rectangle is $$A=$$length$$\times$$breadth.Hence, the length and breadth can both be $$(5a-4)$$ or $$(5a-3)$$.(ii) Let us first factorize the given expression $$24x^2-15x$$ as shown below:$$24x^{ 2 }-15x\\ =x(24x-15)$$Therefore, the area of the rectangle is $$x(24x-15)$$ and we also know that the area of the rectangle is $$A=$$length$$\times$$breadth.Hence, the length and breadth can both be $$x$$ or $$(24x-15)$$.Maths

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