Chapter 11.4, Problem 38PPS

To determine

To calculate: To write an expression to find the length of the rectangle.

Answer to Problem 38PPS

Expression for length of the rectangle is $x^2+3x-18$ .

Explanation of Solution

Given information:

Area of the rectangle $=$ $x^2+2x-24$

Breadth of the rectangle $=$ $\frac{x-4}{x-3}$

Formula Used:

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

Calculation:

Given :

Area of the rectangle $=$ $x^2+2x-24$

Breadth of the rectangle $=$ $\frac{x-4}{x-3}$

Using the above formula, we have:

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

  $x^2+2x-24$

  $=$ Length of the rectangle $\times$

  $\frac{x-4}{x-3}$

Solving further, we have:

  $\left(x-4\right)\left(x+6\right)$

  $=$ Length of the rectangle $\times$

  $\frac{x-4}{x-3}$

Length of the rectangle $=$ $\frac{\left(x-4\right)\left(x+6\right)\left(x-3\right)}{\left(x-4\right)}$

Length of the rectangle $=$ $\frac{\left(x+6\right)\left(x-3\right)}{1}$

Thus, Length of the rectangle $=$ $\left(x+6\right)\left(x-3\right)$

Length of the rectangle $=$ $x^2+3x-18$

Conclusion:

Thus, expression for length of the rectangle is $x^2+3x-18$ .