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

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?

Answer 2

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.