A triangle has a perimeter of 25 inches. The medium side is 7 more than the short side, and the longest side is 4times the length of the shortest side. Find the shortest side.The shortest side isinches.

Let 'x' be the shortest side of this triangle. We know that the medium side is 7 more than the short side, so this is (x + 7). Also, the longest side is 4 times the short side, so this is 4x.

Knowing that the perimeter - which is the sum of all three sides, is 25 inches, we can write an equation for x,

[tex]x+(x+7)+4x=25[/tex]

Add like terms,

[tex]\begin{gathered} (x+x+4x)+7=25 \\ \\ 6x+7=25 \end{gathered}[/tex]

Subtract 7 from both sides,

[tex]\begin{gathered} 6x+7-7=25-7 \\ \\ 6x=18 \end{gathered}[/tex]

And divide both sides by 6,

[tex]\begin{gathered} \frac{6x}{6}=\frac{18}{6} \\ \\ x=3 \end{gathered}[/tex]

Hence, the shortest side of the triangle is 3 inches long.