Question

a triangle has a perimeter represented by the expression $9x + 7$. a square has a side length represented by $4x - 3$. which expression represents the total perimeter of the two figures $25x - 5$ $4x^2 + 9x - 5$ $20x$ $13x + 4$

Explanation:

Step1: Find the perimeter of the square

The perimeter of a square is calculated by the formula \( P = 4\times \text{side length} \). Given the side length of the square is \( 4x - 3 \), so the perimeter of the square is \( 4\times(4x - 3) \).
\[

$$\begin{align*} 4\times(4x - 3)&=4\times4x-4\times3\\ &=16x - 12 \end{align*}$$

\]

Step2: Find the total perimeter of the two figures

The perimeter of the triangle is \( 9x + 7 \), and the perimeter of the square is \( 16x - 12 \). To find the total perimeter, we add these two expressions together: \( (9x + 7)+(16x - 12) \).
\[

$$\begin{align*} (9x + 7)+(16x - 12)&=(9x + 16x)+(7 - 12)\\ &=25x - 5 \end{align*}$$

\]

Answer:

\( 25x - 5 \)