Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

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Solution

(i) $25 a^{2} - 35 a + 12$
$= 25 a^{2} - 20 a - 15 a + 12$
$= 5 a (5 a - 4) - 3 (5 a - 4) = (5 a - 4) (5 a - 3)$
The possible values of length $= (5 a - 3)$ and
breadth $= (5 a - 4) .$

(ii) $35 y^{2} + 13 y - 12$
$= 35 y^{2} + 28 y - 15 y - 12$
$= 7 y (5 y + 4) - 3 (5 y + 4) = (5 y + 4) (7 y - 3)$
The possible values of length $= (7 y - 3)$
and breadth $= (5 y + 4) .$

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Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: Area : 25 $a^{2}$ – 35a + 12

Q. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given :
(i) Area :

25 a^{2} - 35 a + 12

(ii) Area :

35 y^{2} + 13 y - 12

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\begin{matrix} \begin{matrix} A r e a : 25 a^{2} - 35 a + 12 \end{matrix} (i) \end{matrix} \begin{matrix} \begin{matrix} A r e a : 35 y^{2} + 13 y - 12 \end{matrix} (i i) \end{matrix}

Q. Give possible expressions for the length and breadth of the following rectangles, in which their areas are given.
Area:

35 y^{2} + 13 y - 12

Q. Give possible expressions for the length and breadth of the following rectangles, in which their area are given.
Area:

25 a^{2} - 35 a + 12

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Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

(i) 25a2−35a+12=25a2−20a−15a+12=5a(5a−4)−3(5a−4)=(5a−4)(5a−3)The possible values of length =(5a−3) and breadth=(5a−4). (ii) 35y2+13y−12=35y2+28y−15y−12=7y(5y+4)−3(5y+4)=(5y+4)(7y−3)The possible values of length =(7y−3)and breadth=(5y+4).