Question

The area of a rectangle is given by the expression (7x^2-8x-12) square units. What is the length of the rectangle if its width is (x – 2) units?

Answer 1

Given:

Area of the rectangular rug = 7x²-8x-12 square units.

Width of the rectangle = ( x - 2 ) units

To find:

The length of the rectangular rug.

Solution:

Area of a rectangle = Length × Breadth

Given Area of the rectangular rug = 7x²-8x-12 square units

Breadth (Width) = ( x - 2 ) units

So Length = ?

Let the length be y.

A/q (x - 2) (y) = 7x² - 8x - 12

y = ( 7x² - 8x - 12 )/(x - 2)

y=7x+6.

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Answer 2

Step-by-step explanation:

Given:  The Area of the rectangle = $7x^{2} -8x-12$ square units.

Width (Breadth) of the rectangle = $( x - 2 )$ units

To find:  The length of the rectangle

The formula of area of rectangle is,

⇒ $Length\times Breadth = Area\ of rectangle$

Putting the values given in the above equation,

⇒ $Length\times (x-2)=7x^{2} -8x-12$

⇒ $Length= \frac{7x^{2} -8x-12}{(x-2)}$

When we divide  $7x^{2} -8x-12$  by $( x - 2 )$ by long division method, it leaves no remainder and we get the quotient as,

⇒ $Length = 7x+6$

Hence, the length of the rectangle with the given width and area is $7x+6$.