Question

A certain triangle has a perimeter of 3060 mi. The shortest side measures 76 mi less than the middle side, and the longest side measures 373 mi more than the middle side. Find the

lengths of the three sides.
The shortest side ismi long

Answer 1

Shortest side = 921 mi

Middle side = 845 mi

Longest side = 1294 mi

Explanation:

Let x = length of the middle side of the triangle.

Therefore:

• Middle side = x mi
• Shortest side = (x - 76) mi
• Longest side = (x + 373) mi

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a triangle is the sum of the measures of its three sides.

`\begin{aligned}\sf Perimeter & = x + (x-76)+(x+373)\\\implies 3060 & = x + x -76+x+373\\3060 & = x + x+x+373-76\\3060 & = 3x +297\\3060-297 & = 3x +297-297\\2763 & = 3x\\3x & = 2763\\3x / 3 & = 2763 / 3\\x & = 921\end{aligned}`

To find the lengths of the three sides of the triangle, substitute the found value of x into the expression for each side:

`\textsf{Shortest side}=x=\sf 921\:mi`

`\textsf{Middle side}=x-76=\sf 921-76=845\:mi`

`\textsf{Longest side}=x+373=\sf 921+373=1294\:mi`