Question

the length of a rectangle is 6 inches longer than it is wide. if the area is 160 square inches, what are the dimensions of the rectangle? the width, or shorter side is inches the length, or longer side is inches

Explanation:

Step1: Let the width be $x$ inches.

The length is $x + 6$ inches.

Step2: Use the area formula for rectangle.

The area formula is $A=\text{length}\times\text{width}$. So, $160=(x + 6)x=x^{2}+6x$.

Step3: Rearrange to quadratic - form.

We get the quadratic equation $x^{2}+6x - 160 = 0$.

Step4: Factor the quadratic equation.

$x^{2}+6x - 160=(x + 16)(x - 10)=0$.

Step5: Solve for $x$.

Setting each factor equal to zero gives $x+16 = 0$ or $x - 10=0$. So, $x=-16$ or $x = 10$. Since the width cannot be negative, we take $x = 10$.

Step6: Find the length.

The length is $x + 6=10 + 6 = 16$ inches.

Answer:

The width, or shorter side is 10 inches
The length, or longer side is 16 inches