Question

“Straight Ahead” isn’t part of the problem, that is just what this section of the problem is called.

Answer 1

To find the perimeter in terms of x, follow the steps below.

Step 01: Factor out the quadratic equation.

To do it, find its roots using the quadratic formula.

For a quadratic equation y = ax² + bx + c, the quadratic formula is:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

In this question:

a = 1

b = 8

c = 16

Then:

$\begin{gathered} x=\frac{-8\pm\sqrt[]{8^2-4\cdot1\cdot16}}{2\cdot1} \\ x=\frac{-8\pm\sqrt[]{64-64}}{2} \\ x=\frac{-8\pm\sqrt[]{0}}{2} \\ x_1=\frac{-8-0}{2}=-\frac{8}{2}=-4 \\ x_2=\frac{-8+0}{2}=-\frac{8}{2}=-4 \end{gathered}$

A quadratic equation in the factored form is y = (x - x₁)(x - x₂), where x₁ and x₂ are the roots.

Then, the quadratic equation can be written as:

$\begin{gathered} (x-(-4))\cdot(x-(-4)) \\ (x+4)\cdot(x+4) \end{gathered}$

Step 02: Find the sides of the rectangle.

The area of the rectangle is:

$A=(x+4)\cdot(x+4)$

A rectangle with sides "a" and "b" has an area (A):

$A=a\cdot b$

Then, the sides of the triangle are:

a = x + 4

b = x + 4

Step 03: Find the perimeter.

A rectangle with sides "a" and "b" has the perimeter (P):

$P=2a+2b$

Since:

a = x + 4

b = x + 4

Then,

$P=2\cdot(x+4)+2\cdot(x+4)$

Solving the equation:

$\begin{gathered} P=2x+8+2x+8 \\ P=4x+16 \end{gathered}$

Answer:

The perimeter (P) is:

$P=4x+16$