Question

the area of a rectangular wall of a barn is 91 square feet. its length is 6 feet longer than the width. find the length and width of the wall of the barn. the width is feet.

Explanation:

Step1: Let the width be $x$ feet.

The length is $x + 6$ feet. The area formula for a rectangle is $A=\text{length}\times\text{width}$. So we have the equation $x(x + 6)=91$.

Step2: Expand the left - hand side.

$x^{2}+6x=91$, then rewrite it in standard quadratic form $x^{2}+6x - 91=0$.

Step3: Factor the quadratic equation.

We need to find two numbers that multiply to - 91 and add up to 6. The numbers are 13 and - 7. So $x^{2}+6x - 91=(x + 13)(x - 7)=0$.

Step4: Solve for $x$.

Setting each factor equal to zero gives $x+13 = 0$ or $x - 7=0$. So $x=-13$ or $x = 7$. Since the width cannot be negative, we discard $x=-13$.

Answer:

7