Respuesta :
shortest side: 851
middle side:927
longest side : 1306
Explanation
Step 1
Let
x represents the shortest side
y represents the middle side
z represents the longest side
so, set the equations
a) the perimeter of a rectangle is the sum of the sides, so
[tex]\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}[/tex]b) The shortest side measures 76 mi less than the middle side( in other words, you have to subtract 76 from middle side to get the shortest side)
[tex]x=y-76\Rightarrow equation(2)[/tex]c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)
[tex]z=y+379\Rightarrow equation(3)[/tex]Step 2
solve the equations
a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)
[tex]\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}[/tex]now, replace the y value in equatino (2) to find x
b)
[tex]\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}[/tex]c) finally, prelace x and y value in equation (1) to find z
[tex]\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}[/tex]so
shortest side: 851
middle side:927
longest side : 1306
I hope this helps you
