Perimeter of an isosceles triangle

Question

The shortest side of an isosceles triangle is 3x-5. The two longer sides are 10 inches longer than the shortest side. The perimeter of the triangle is 50 inches. What is the length of each of the longer sides of the triangle?

Answer 1

Since the longer side is 10 inches more than the shortest side (3x-5) , then we can write the following expression for the length of each longer side:

3x - 5 + 10 This is equivalent to 3x + 5.

Since the perimeter of the triangle is 50 inches , we can add the three expressions that represent each of the sides and determine the value of x:

Shortest side + one long side + one long side = 50 inches

3x - 5 + 3x + 5 + 3x +5 = 50

Now combine like terms and use inverse operations to find x:

9x + 5 = 50

9x + 5 -5 = 50 -5

9x = 45

9x/9 = 45/9

x=5

Therefore, the longer sides are each 3x - 5 + 10 OR 3*5 -5 + 10 = 15 - 5 + 10 = 10 + 10 =20 inches each