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?
First, we are going to solve the equation [tex] (x-13)(x+8)=196 [/tex] to find the value of [tex] x [/tex].
Let's solve the equation step by step
Step 1. Use the distributive property to destroy the parenthesis:
[tex] (x-13)(x+8)=196 [/tex]
[tex] x^2+8x-13x-104=196 [/tex]
[tex] x^2-5x-104=196 [/tex]
Step 2. Subtract 196 to both sides of the equation:
[tex] x^2-5x-104-196=196-196 [/tex]
[tex] x^2-5x-300=0 [/tex]
Step 3. Factor the expression:
[tex] (x+15)(x-20)=0 [/tex]
Step 4. Set each factor equal to zero and solve for [tex] x [/tex]:
[tex] x+15=0 [/tex] or [tex] x-20=0 [/tex]
[tex] x=-15 [/tex] or [tex] x=20 [/tex]
Since we are dealing with lengths here, and lengths cannot be negative, the only valid solution is [tex] x=20 [/tex]
Now, we know from our problem that the missing side of the rectangle is given by the expression [tex] x+8 [/tex], so to find the actual length, we just need to replace [tex] x [/tex] with 8 in the given expression and simplify:
[tex] Missing.Length=x+8 [/tex]
[tex] Missing.Length=20+8 [/tex]
[tex] Missing.Length=28 [/tex] units
We can conclude that the missing side length represented by x + 8 units of the rectangle is 28 units.
