Question

Calculate the perimeter of a rectangle whose area is
$\bf Area = 25x^2-35x+12$

Answer 1

Answer:

• Perimeter of rectangle is  ( 20x - 14 ).

Step-by-step explanation:

Given : Area of rectangle is 25x²-35x+12

To find : Perimeter of rectangle

Solution :

Here in this question, concept of factorisation is used. We are given the area of rectangle in the form of quadratic equation and we are asked to find the perimeter of rectangle. Firstly we have to factorise the given equation so that we could obtain the value of its dimensions and then by applying formula for perimeter of rectangle, we will get our answer. So let's proceed by factorising the equation !

We have formula for area of rectangle::

→ Area of rectangle = length × breadth

→ 25x² - 35x + 12 = length × breadth

→ 25x² - 15x - 20x + 12 = length × breadth

→ 5x ( 5x - 3 ) - 4 ( 5x -3 ) = length × breadth

→ ( 5x - 4 ) ( 5x - 3 ) = length × breadth

So either length and breadth of rectangle will be (5x - 4) (5x-3).

Now we have formula for perimeter of rectangle::

→ Perimeter of rectangle = 2 ( length + breadth )

→ Perimeter of rectangle = 2 [ ( 5x - 4 ) + ( 5x - 3 ) ]

→ Perimeter of rectangle = 2 [ 5x - 4 + 5x - 3 ]

→ Perimeter of rectangle = 2 [ 5x + 5x - 4 - 3 ]

→ Perimeter of rectangle = 2 [ 10x - 7 ]

→ Perimeter of rectangle = 20x - 14

So the perimeter of rectangle is ( 20x - 14 ).