Answer:
For the triangle, [tex]x=14[/tex]
For the rectangle, [tex]x=\frac{5}{2}[/tex]
Step-by-step explanation:
To solve for x in these equations, we have treat each side as it's just one number - add them all up.
The perimeter of a triangle will be the sum of all 3 of its sides.
So:
[tex]x + 4 + 2x - 3 + x = 57[/tex]
We can combine like terms to get
[tex]4x + 1 = 57[/tex]
Subtract 1 from both sides:
[tex]4x = 56[/tex]
Divide both sides by 4:
[tex]x = 14[/tex]
For the rectangle, the perimeter is [tex]2l + 2w[/tex], so we can add up the sides.
[tex]5x - 4 + 5x - 4 + 3x + 2 + 3x + 2 = 36[/tex]
Combine like terms:
[tex]16x - 4 = 36[/tex]
Add 4 to both sides:
[tex]16x = 40[/tex]
Divide both sides by 18:
[tex]x = \frac{40}{16}[/tex]
Simplifying this fraction gets us
[tex]\frac{5}{2}[/tex]
Hope this helped!
