Q48. - Algebra 1

Question

Write an expression to represent the perimeter of the triangle. Then find the perimeter if $\mathit{x}\mathbf{=}\mathbf{2}$ and $\mathit{y}\mathbf{=}\mathbf{7}$.

Step-by-Step Solution

Answer

The perimeter of the triangle is .$\mathbf{49}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}unit}}$

Step 1 – Given information.

The given value is:

$x=2,y=7$

 And sides of the triangle are $4+5x,4+5x,3y$.

Step 2 – Write the concept.

The perimeter of the triangle is the sum of all sides so add all the side lengths to obtain the perimeter of the triangle.

Step 3 – Write the perimeter.

The perimeter of the triangle is given in below:

$\begin{array}{c}P=4+5x+4+5x+3y\\ =4+4+5x+5x+3y\\ =8+10x+3y\end{array}$

Step 4 – Evaluate the expression.

Substitute $x=2,y=7$ in the equation $P=8+10x+3y$.

$\begin{array}{c}P=8+10x+3y\\ =8+10\left(2\right)+3\left(7\right)\\ =8+20+21\\ =28+21\\ =49\end{array}$