Question

the width of a rectangle when the area is x^2-x-72 and the length is x+8

Answer 1

Answer:

x - 9...

Step-by-step explanation:

in photo..

hope it helps!!

Answer 2

$\boxed{\sf \red{x-9 = Length} }$

Given:

• Length of the rectangle = $\sf { x+8}$

• Area of the rectangle = $\sf { x^2 - x - 72}$

To calculate:

• Width of the rectangle.

Calculation:

As we know that,

$\underline{ \boxed{ \pmb{\sf { {{Area}_{(Rectangle)} = Length \times Width}} }} }$

According to the question,

$\longrightarrow \sf {x^2 - x - 72 = Length \times x+8 }$

$\longrightarrow \sf {\dfrac{x^2 - x - 72}{x+8} = Length }$

Now, we have to divide a polynomial by a polynomial. We'll find our answer by long division method :

(Performing division) :

$\large\begin{gathered} \\ \: \: \sf{x - 9} \over \sf{x + 8 \Big) \: {x}^{2} - x - 72 }\\ \sf{ \: \: \: {x}^{2} + 8x } \\ \begin{gathered} - \: \: \: \: \: \: - \over \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 9x - 72} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ - 9x - 72} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \: \: \: \: \: \: \: \: + \: \over \: \: \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0} \end{gathered} \end{gathered}$

$\longrightarrow \boxed{\sf \red{x-9 = Length} }$

Therefore, length of the rectangle is (x-9).

Verification:

→ Area of rectangle = Length × Width

LHS:

→ Area of rectangle = x² - x - 72

RHS:

→ Length × Width

→ (x + 8)(x -9)

→ x(x - 9) + 8(x - 9)

→ x² - 9x + 8x - 72

→ x² - x - 72

• LHS = RHS,

Hence, verified!