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: Recall rectangle - area formula

Let the width be $w$, then the length $l = w + 6$. The area formula of a rectangle is $A=l\times w$. Substituting the values, we get $40=(w + 6)\times w$, which simplifies to $w^{2}+6w−40 = 0$.

Step2: Factor the quadratic equation

We factor $w^{2}+6w - 40=0$ as $(w + 10)(w - 4)=0$.

Step3: Solve for the width

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

Step4: Solve for the length

If $w = 4$, then $l=w + 6=4 + 6=10$.

Answer:

10 by 4