Question

Area of rectangle is represented by the expression (m^2 – 7m + 12) sq.units . Find the breadth of the rectangle if it's length is represented by (m – 4) units.
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Answer 1

Given :

• Area of the Rectangle = (m² - 7m + 12) units².

• Length of the Rectangle = (m - 4)

To Find :

The breadth of the Rectangle.

Solution :

Let the breadth of the Rectangle be x units.

Now , using the formula for area of a Rectangle and Substituting the values in it , we get :

$\boxed{\underline{:\implies \bf{A = Length \times x}}}$

$:\implies \bf{(m^{2} - 7m + 12 ) = (m - 4) \times x}$

By Factorizating (m² - 7m + 12) , we get :

(Using middle-splitting theorem)

$:\implies \bf{(m^{2} - (4 + 3)m + 12) = (m - 4) \times x}$

$:\implies \bf{(m^{2} - 4m - 3m + 12) = (m - 4) \times x}$

$:\implies \bf{m(m - 4) - 3(m - 4) = (m - 4) \times x}$

$:\implies \bf{(m - 4)(m - 3) = (m - 4) \times x}$

Now dividing (m - 4) on both the sides , we get :

$:\implies \bf{\dfrac{(m - 4)(m - 3)}{(m - 4)} = \dfrac{(m - 4)}{(m - 4)} \times x}$

$:\implies \bf{(m - 3) = 1 \times x}$

$:\implies \bf{(m - 3) = x}$

$\underline{\therefore \bf{Breadth\:(x) = (m - 3)\: units}}$

Hence, the breadth of the Rectangle is (m - 3).

Answer 2

Answer:

Area of rectangle is represented by the expression (m^2 – 7m + 12) sq. units . Find the breadth of the rectangle if it's length is represented by (m – 4) units.

Step-by-step explanation: