Q4. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Express the perimeter of the rectangle below polynomial.

F $3x^2-4x+7$

G $3x^2+x+7$

H $6x^2-8x+14$

J $6x^2-4x+7$

Step-by-Step Solution

Answer

The perimeter of the given rectangle is $6x^2-8x+14$. Therefore, the option H is correct.

Step 1. Write the formula for the perimeter of the rectangle.

The perimeter $\left(P\right)$ of the rectangle is given by:

$P=2\left(L+B\right)$

Where $L$ and $B$ are the length and breadth of the rectangle respectively.

Step 2. Express the perimeter of the given rectangle in polynomial.

The given diagram of the rectangle is:

From the given diagram of the rectangle, it can be noticed that the length and breadth of the triangle are $2x^2-x+3$ and $x^2-3x+4$ respectively.

Therefore, the values of $L$ and $B$ are $2x^2-x+3$ and $x^2-3x+4$ respectively.

Substitute the values of $L$ and $B$ in the formula of the perimeter of the rectangle.

Therefore, it is obtained that:

$$\begin{gathered} P=2\left(L+B\right) \\ =2\left(2x^2-x+3+x^2-3x+4\right) \\ =2\left(2x^2+x^2-x-3x+3+4\right) \\ =2\left(3x^2-4x+7\right) \\ =6x^2-8x+14 \end{gathered}$$

Therefore, the perimeter of the given rectangle in polynomial is $6x^2-8x+14$. Therefore, the option H is correct.