Question

5.5: homework assignment score: 2/33 answered: 2/33 question 31 the length of a rectangle is 7 inches longer than it is wide. if the area is 78 square inches, what are the dimensions of the rectangle? the width, or shorter side is inches the length, or longer side is inches question help: video

Explanation:

Step1: Let the width be $x$ inches.

The length is $x + 7$ inches.

Step2: Use the area formula for rectangle.

The area formula of a rectangle is $A=\text{length}\times\text{width}$. So we have the equation $x(x + 7)=78$.

Step3: Expand the equation.

$x^{2}+7x = 78$, which can be rewritten as $x^{2}+7x-78=0$.

Step4: Factor the quadratic equation.

We factor $x^{2}+7x - 78$ into $(x + 13)(x - 6)=0$.

Step5: Solve for $x$.

Setting each factor equal to zero gives $x+13 = 0$ or $x - 6=0$. So $x=-13$ or $x = 6$. Since the width cannot be negative, we take $x = 6$.

Step6: Find the length.

The length is $x+7=6 + 7=13$ inches.

Answer:

The width, or shorter side is 6 inches.
The length, or longer side is 13 inches.