Problem: Calculate the perimeter of rectangle whose area is 25x²-35x+12?

Solution:

We know that the area of the rectangle is given by the product of its length and its breadth. So, if l and b are the length and breadth of the rectangle respectively, then we have:

Area of rectangle = l x b

Given that the area of the rectangle is 25x²-35x+12, we can write:

l x b = 25x²-35x+12

Now, we need to find the perimeter of the rectangle. The perimeter of a rectangle is given by the sum of its four sides. If l and b are the length and breadth of the rectangle respectively, then we have:

Perimeter of rectangle = 2(l + b)

We can use the given area and the formula for perimeter to form two equations in l and b, and then solve for l and b. Here's how:

Step 1: Find the factors of 25x²-35x+12

25x²-35x+12 = 25x²-20x-15x+12
= 5x(5x-4)-3(5x-4)
= (5x-4)(5x-3)

So, we have:

l x b = (5x-4)(5x-3)

Step 2: Express the perimeter in terms of l and b

Perimeter of rectangle = 2(l + b)
= 2((5x-4) + (5x-3))
= 2(10x-7)
= 20x-14

Step 3: Substitute the value of l x b from Step 1 into the formula for perimeter in Step 2

Perimeter of rectangle = 20x-14
= 2(l + b)
= 2((5x-4) + (5x-3))
= 2(10x-7)
= 20x-14

Therefore, the perimeter of the rectangle is 20x-14.

Conclusion: The perimeter of the rectangle whose area is 25x²-35x+12 is 20x-14.

Area of rectangle = 25x^2– 35x + 12

We know, area of rectangle = length × breadth

So, by factoring 25x^2– 35x + 12, the length and breadth can be obtained.

25x^2– 35x + 12 = 25x^2– 15x – 20x + 12

=> 25x^2– 35x + 12 = 5x(5x – 3) – 4(5x – 3)

=> 25x^2– 35x + 12 = (5x – 3)(5x – 4)

So, the length and breadth are (5x – 3)(5x – 4).

Now, perimeter = 2(length + breadth)

perimeter of the rectangle = 2[(5x – 3)+(5x – 4)]

= 2(5x – 3 + 5x – 4) = 2(10x – 7) = 20x – 14

Thus, the perimeter = 20x – 14


Thanks