Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area : 25a 2 – 35a + 12
(ii) Area : 35y 2 + 13y –12
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area : 25a 2 – 35a + 12
(ii) Area : 35y 2 + 13y –12
Solution and Explanation
Area = Length × Breadth
The expression given for the area of the rectangle has to be factorised. One of its factors will be its length and the other will be its breadth.
(i) 25a 2 – 35a + 12 = 25a2 - 15a - 20a + 12
= 5a(5a - 3) - 4 (5a - 3)
= (5a - 3) (5a - 4)
Therefore, possible length = 5a - 3
And, possible length = 5a - 4
(ii) 35y 2 + 13y –12 = 35y2 + 28y - 15y - 12
= 7y(5y + 4) - 3 (5y + 4)
= (5y + 4)(7y - 3)
Therefore, possible length = 5y + 4
And, possible breadth = 7y - 3
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