Question

Calculate the perimeter of a rectangle whose area is 25x2 – 35x + 12. 

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Answer 1

Answer:

Step-by-step explanation:

The perimeter = 20x – 14

Step-by-step explanation:

Given,

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)

So, perimeter of the rectangle = 2((5x – 3)+(5x – 4)) = 2(5x – 3 + 5x – 4) = 2(10x – 7) = 20x – 14

So, the perimeter = 20x – 14.

Step-by-step explanation:

Answer 2

Answer:

$area \: of \: rectangle = 25 {x}^{2} - 35x + 12 \\ \\ \\ l \times b = 25 {x}^{2} - 15x - 20x + 12 \\ \\ \\l \times b = 5x(5x - 3) - 4(5x - 3) \\ \\ \\ l \times b= (5x - 3)(5x - 4) \\ \\ \\ l = 5x - 3 \\ \\ \\ \\ b = 5x - 4 \\ \\ \\ \\ perimeter = 2(l + b) \\ \\ \\ \\ = 2(5x - 3 + 5x - 4) \\ \\ \\ \\ = 2(10x - 7) \\ \\ \\ \\ = (20x - 14)$