Question

Give possible expressions for the length and breadth of the rectangle whose areas is given by 25a^2 -35a+12

Answer 1

Answer:

Length=(5a-3)

Breadth=(5a-4)

Step-by-step explanation:

25a^2 - 35a + 12

25a^2 - 15a - 20a + 12

5a(5a-3) - 4(5a-3)

(5a-3)(5a-4)

Length=(5a-3)

Breadth=(5a-4)

Answer 2

$\Large{\underline{\underline{\bf{Solution}}}}$

$we \: know \: that \\ \\ area \: of \: triangle = length \: \times \: breadth \\ \\ we \: have \\ \\ area = 25 {a}^{2} - 35a + 12 \\ \\ area = 25 {a}^{2} - 20a - 15a + 12 \\ \\ area \: = (25 {a}^{2} - 20a) - (15a - 12) \\ \\ area = 5a(5a - 4) - 3(5a - 4) \\ \\ area = (5a - 4)(5a - 3) \\ \\ hence \: the \: possible \: expression \: for \: the \: length \: and \: breadth \: are \\ \\ length = (i) \: 5a - 4 \: \: (ii) \: 5a - 3 \\ \\ breadth \: = (i) \: 5a - 3 \: (ii) \: 5a - 4$

$\Large{\underline{\underline{\bf{Thanks}}}}$