Question

a rectangle has an area of 40 square units. the length is 6 units greater than the width. what are the dimensions of the rectangle? 8 by 5 10 by 4 11 by 9 13 by 7

Explanation:

Step1: Let width be $x$.

Length is $x + 6$. Area formula for rectangle is $A=\text{length}\times\text{width}$, so $40=(x + 6)x$.

Step2: Expand the equation.

$40=x^{2}+6x$, which can be rewritten as $x^{2}+6x - 40=0$.

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, $x = 4$. Then length is $x + 6=4 + 6 = 10$.

Step5: Check options.

The dimensions are 10 by 4.

Answer:

10 by 4