clara writes the equation (x - 13)(x + 8) = 196 to solve for the missing side length of a rectangle…

Explanation:

Step1: Expand the left - hand side

$(x - 13)(x + 8)=x^{2}+8x-13x - 104=x^{2}-5x - 104$. So the equation becomes $x^{2}-5x - 104 = 196$.

Step2: Rearrange to standard quadratic form

$x^{2}-5x-104 - 196=0$, which simplifies to $x^{2}-5x - 300 = 0$.

Step3: Factor the quadratic equation

$x^{2}-5x - 300=(x - 20)(x + 15)=0$.

Step4: Solve for x

Setting each factor equal to zero gives $x - 20 = 0$ or $x+15 = 0$. So $x = 20$ or $x=-15$. Since side - length cannot be negative, we take $x = 20$.

Step5: Find the value of $x + 8$

Substitute $x = 20$ into $x + 8$, we get $20+8=28$.

Answer:

D. 28