a rectangle has an area of 40 square units. the length is 6 units greater than the width. what are the…

Explanation:

Step1: Let the width be $x$.

The length is $x + 6$.

Step2: Use the area formula.

The area of a rectangle $A=length\times width$, so $40=(x + 6)\times x$, which simplifies to $x^{2}+6x - 40=0$.

Step3: Factor the quadratic equation.

$x^{2}+6x - 40=(x + 10)(x - 4)=0$.

Step4: Solve for $x$.

Setting each factor equal to zero gives $x+10 = 0$ or $x - 4=0$. So $x=- 10$ or $x = 4$. Since width cannot be negative, $x = 4$.

Step5: Find the length.

The length is $x + 6=4 + 6=10$.

Answer:

10 by 4