Question

Give possible expression for the length and breadth of each of the following rectangle in which their areas are given
Area 25a squ-35a+12​

Answer 1

Answer:

Given area 25a²-35a+12

= 25a²-15a-20a+12

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

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

This is the expression for length and breadth of a rectangle

bcz Area = length * breadth

Answer 2

Question:

Given the possible expression for the length and breadth of each of the following rectangle in which their areas are given.

Area 25a² - 35a + 12

Answer

Length of rectangle is (5a - 4) and breadth is (5a - 3)

Explanation

Given the area is 25a² - 35a + 12

The above equation is in the form ax² + bx + c.

We can solve it by splitting the middle term in such a way their sum is b (-35) and the product is ac (25*12).

Now, by splitting the middle term

→ 25a² - 35a + 12

→ 25a² - 20a - 15a + 12

→ 5a(5a - 4) -3(5a - 4)

→ (5a - 4) (5a - 3)

By splitting the given area i.e. 25a² - 35a + 12 we get, (5a - 4)(5a - 3)

According to the question, we have to find the length and breadth of the rectangle.

Now, Area of rectangle = length × breadth

And what we get is (5a - 4)(5a - 3)

So,

Length of rectangle = (5a - 4)

Breadth of rectangle = (5a - 3)

We will take the positive value of a because negative values (of length and breadth) are not possible.

And for the positive value of a: (5a - 4) < (5a - 3)