Question

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle? 7 15 20 28

Answer 1

First, we are going to solve the equation $(x-13)(x+8)=196$ to find the value of $x$.

Let's solve the equation step by step

Step 1. Use the distributive property to destroy the parenthesis:

$(x-13)(x+8)=196$

$x^2+8x-13x-104=196$

$x^2-5x-104=196$

Step 2. Subtract 196 to both sides of the equation:

$x^2-5x-104-196=196-196$

$x^2-5x-300=0$

Step 3. Factor the expression:

$(x+15)(x-20)=0$

Step 4. Set each factor equal to zero and solve for $x$:

$x+15=0$ or $x-20=0$

$x=-15$ or $x=20$

Since we are dealing with lengths here, and lengths cannot be negative, the only valid solution is $x=20$

Now, we know from our problem that the missing side of the rectangle is given by the expression $x+8$, so to find the actual length, we just need to replace $x$ with 8 in the given expression and simplify:

$Missing.Length=x+8$

$Missing.Length=20+8$

$Missing.Length=28$ units

We can conclude that the missing side length represented by x + 8 units of the rectangle is 28 units.

Answer 2

 The Answer is 28.

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?