Question

A rectangle has an area of 45x2 − 42x − 48 and a width of 5x − 8. What is the length of the rectangle?

Answer 1

Answer:

$3(3x+2)=9x+6$ units.

Step-by-step explanation:

We have been given that a rectangle has an area of $45x^2-42x-48$ and a width of $5x-8$. We are asked to find the length of the rectangle.

Since we know that area of a rectangle equals to the product of its width and length, so to find the length of our given rectangle we will divide area of the rectangle by its width.

$\text{Length of rectangle}=\frac{45x^2-42x-48}{5x-8}$

$\text{Length of rectangle}=\frac{3(15x^2-14x-16)}{5x-8}$        

$\text{Length of rectangle}=\frac{3(15x^2+10x-24x-16)}{5x-8}$

$\text{Length of rectangle}=\frac{3(5x(3x+2)-8(3x+2))}{5x-8}$  

$\text{Length of rectangle}=\frac{3((3x+2)(5x-8))}{5x-8}$  

Upon cancelling $5x-8$ from numerator and denominator we will get,

$\text{Length of rectangle}=3(3x+2)$  

$\text{Length of rectangle}=9x+6$  

Therefore, the length of the rectangle is $3(3x+2)=9x+6$ units.

Answer 2

Dividend

Divisor

and

9x+6