Use the information to solve the problems below. a. The longest side of a triangle is six more units than the shortest side. The third side is twicethe length of the shortest side. If the perimeter of the triangle is 25 units, write and solve an equation to find the lengths of all three sides of the triangle.

You want the lengths of the sides of a triangle with a perimeter of 25 units such that the longest side is 6 units more than the shortest, and the third side is twice the shortest.

Setup

If we let s represent the shortest side, then the other two sides are ...

s +6
2s

The perimeter is the sum of side lengths ...

p = s +(s +6) +(2s) . . . . . . . . use the expressions for side lengths

25 = 4s +6 . . . . . . . . . . . simplify; use the value of the perimeter

Solution

The solution to the equation is ...

19 = 4s

s = 19/4 = 4.75

s +6 = 10.75

2s = 9.50

The shortest side is 4.75 units; the longest is 10.75 units; and the third side is 9.50 units.