Question

give possible expression for length and breadth of a rectangle whose area is given by 25a ^2-35a +12​

Answer 1

Answer:

Step-by-step explanation:

=> 25a²-35a+12 = 0

=> 25a²-20a-15a+12 = 0

=> 5a(5a-4) - 3(5a-4) = 0

=> (5a-4) (5a-3) = 0

=> a = 4/5 or a = 3/5

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$

$\underline{\underline{ \bold{ \: \: GIVEN \: \: : }}} \to \\ \\ \bold{Area \: \: of \: \: the \: \: rectangle = 25a {}^{2} - 35a + 12} \\ \\ \underline {\underline{ \bold{ \: \: TO \: \: FIND \: \: : }}} \to \\ \\ \bold{ \: Length \: \: and \: \: Breadth \: \: of \: \: the \: \: rectangle}$

$\bold{Now,} \\ \\ \bold{25a {}^{2} - 35a + 12 } \\ \\ \bold{ = 25a {}^{2} - 20a - 15a + 12 } \\ \\ \bold{ = 5a(5a - 4) - 3(5a - 4)} \\ \\ \bold{ = (5a - 4)(5a - 3)}$

$\underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \boxed{\bold{Area \: \: of \: \: a \: \: rectangle = Length \times Breadth}} \\ \\ \bold{Here,} \\ \\ \bold{Area \: \: of \: \: the \: \: rectangle = 25a {}^{2} - 35a + 12} \\ \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (5a - 4)(5a - 3)} \\ \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = Length \times Breadth}$

$\bold{Hence,} \\ \\ \bold{The \: \: posible \: \: expression \: \: of \: \: length \: \: and} \\ \bold{breadth \: \: of \: \: the \: \:rectangle \: \: which \: \: area } \\ \bold{is \: \: 25a {}^{2} - 35a + 12 \: \: are \: : } \\ \bold{ \underline{ \pink{ \: \:(5 a - 4) \: \: and(5a - 3) \: \: }}}$