Answer:
[tex]\textsf{1)}\quad 8x - 20[/tex]
[tex]\textsf{2)}\quad -2x^2 + 2x + 72[/tex]
[tex]\textsf{3)}\quad 18x - 54[/tex]
Step-by-step explanation:
The perimeter of a rectangle is calculated by adding the lengths of all four sides.
In a rectangle, opposite sides are equal in length. Therefore, the perimeter (P) is the sum of two widths (W) and two lengths (L), expressed by the formula:
[tex]P=2(W+L)[/tex]
To find the perimeter of each rectangle, substitute the given width and length into the perimeter formula.
[tex]\hrulefill[/tex]
Given width and length:
[tex]W = 3x+4[/tex]
[tex]L=x-14[/tex]
Substitute the given width and length into the perimeter formula and simplify:
[tex]\begin{aligned}P&=2(3x+4+x-14)\\\\P&=2(4x-10)\\\\P&=8x-20\end{aligned}[/tex]
Therefore, the perimeter of the rectangle is (8x - 20) centimeters.
[tex]\hrulefill[/tex]
Given width and length:
[tex]W = x+6[/tex]
[tex]L=-x^2+30[/tex]
Substitute the given width and length into the perimeter formula and simplify:
[tex]\begin{aligned}P&=2(x+6-x^2+30)\\\\P&=2(-x^2+x+36)\\\\P&=-2x^2+2x+72\end{aligned}[/tex]
Therefore, the perimeter of the rectangle is (-2x² + 2x + 72) centimeters.
[tex]\hrulefill[/tex]
Given width and length:
[tex]W = -x+15[/tex]
[tex]L=10x-42[/tex]
Substitute the given width and length into the perimeter formula and simplify:
[tex]\begin{aligned}P&=2(-x+15+10x-42)\\\\P&=2(9x-27)\\\\P&=18x-54\end{aligned}[/tex]
Therefore, the perimeter of the rectangle is (18x - 54) centimeters.
Answer:
To find the perimeter of a rectangle, you can use the formula:
Perimeter= 2 × ( length + width )
Now, let's find the perimeter for each given rectangle:
1. Width: 3x+4, Length: x-14
2 × (( x − 14) + (3x + 4))
= 2 × (4x − 10)
= 8x − 20
2. Width: x+6, Length: -x^2+30
2 × ((−x² + 30) + (x + 6))
= 2 × (−x² + x + 36)
= −2x ² + 2x + 72
3. Width: -x+15, Length: 10x-42
2 × (( 10x − 42) + ( −x + 15 ))
= 2 × ( 9x − 27)
= 18x −54
Therefore, the perimeters of the given rectangles are:
Step-by-step explanation:
