Geometry of Triangles

Question

The perimeter of a triangle is 105 inches. The longest side is 22 inches longer than the shortest side. The sum of the lengths of the two shorter sides is 15 inches more than the length of the longest side. Find the lengths of the sides of the triangle.

Answer 1

Here's what we know:

a + b + c = 105

c = a + 22

c + 15 = a + b

 

Let's use the second value to put into our equation as that removes two variables:

c + 15 + c = 105

2c + 15 = 105

2c = 90

c = 45 in

 

Now that we know c, we can figure out the other parts:

45 = a + 22

23 = a in

 

23 + b = 45 + 15

23 + b = 60

b = 37 in

 

Now to check:

45 + 23 + 37 = 105

45 + 60 = 105

105 = 105