Question

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

(i) Area = 25a² - 35a + 12

(ii) Area = 35y² + 13y - 12

Need well explained answer.

Answer 1

Answer-

Area of rectangle= length×breadth

i) Area= 25a²-35a+12

l×b= 25a²- (20+15)a + 12

l×b= 25a² -20a 15a +12

l×b= 5a(5a-4)-3(5a-4)

l×b= (5a-3)(5a-4)

Therefore, l= (5a-3), b=(5a-4)

ii) Area= 35y²+13y-12

l×b= 35y²+28y-15y-12

l×b= 7y(5y+4)-3(5y+4)

l×b= (7y-3)(5y+4)

Therefore, l= (7y-3) , b= (5y+4)

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Answer 2

We know,

Area of Rectangle = length × breadth

(i)

According to Question,

l × b = 25a² - 35a + 12

⇒ l × b = 25a² - (20 + 15)a + 12

⇒ l × b = 25a² - 20a - 15a + 12

⇒ l × b = 5a(5a - 4) - 3(5a - 4)

⇒ l × b = (5a - 3) (5a - 4)

Hence,

Length = (5a - 3) & Breadth = (5a - 4)

(ii)

According to Question,

l × b = 35y² + 13y - 12

⇒ l × b = 35y² + (28 - 15)y - 12

⇒ l × b = 35y² + 28y - 15y - 12

⇒ l × b = 7y(5y + 4) - 3(5y + 4)

⇒ l × b = (7y - 3) (5y + 4)

Hence,

Length = (7y - 3) & Breadth = (5y + 4)

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