Question

Calculate the perimeter of a rectangle whose area is 25x² – 35x + 12. 
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Answer 1

$\red {\huge {\underline{ \frak{Your \: answEr : }}}}$

$\green{\large{ \underline{\mathcal{\star \:Given : }}}}$

• Area of Rectangle = 25x² – 35x + 12

$\green{\large{ \underline{\mathcal{\star \: To \: Find : }}}}$

• Perimeter of the Rectangle.

$\green{\large{ \underline{\mathcal{\star \: Solution : }}}}$

$\blacksquare \: \scriptsize\boxed {\bold{Area \: of \: Rectangle = Length \times Breadth}}$

So, By Factoring 25x² – 35x + 12, the Length and Breadth can be obtained.

$\large \leadsto \tt{25 {x}^{2} - 35x + 12 = 0}$

$\large \leadsto \tt{25 {x}^{2} - 15x - 20x + 12 = 0}$

$\large \leadsto \tt{5x(5x - 3) - 4(5x - 3) = 0}$

$\pink{\large \leadsto \tt{(5x - 3)(5x - 4) = 0}}$

So, the Length and Breadth are (5x – 3)(5x – 4).

$\blacksquare \: \scriptsize\boxed {\bold{Perimeter = 2(Length + Breadth)}}$

$\large \leadsto \tt{Perimeter= 2(5x - 3 + 5x - 4)}$

$\orange{\large \leadsto \boxed{\tt{Perimeter= 2(10x - 7)}}}$

$\huge{\red{\ddot{\smile}}}$

Answer 2

Answer:

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.