Lesson 2: Pythagorean Theorem Problem Solving - The 3: 4: 5 Triangle Example 2


EXAMPLE 2

A carpenter may double each of the side lengths of a 3: 4: 5 triangle in order to be more accurate in determining if the walls are square. Does doubling each of the side lengths affect whether the triangle remains a right triangle?

Solution


Step 1: Draw and label the diagram.



Step 2: Calculate the square of the longest side.

The longest side is 10 units long

c2 = 102
= 100 square units

Step 3: Calculate the sum of the squares of the other two sides

The other two sides, a and b, are 6 and 8.

a2 + b2 = 62 + 82
= 36 + 64
= 100 square units

Because both sides of the equations are 100 square units, this triangle is a right triangle. Doubling the length of each side does not change the type of triangle.

Alternate Solution


You can also do these calculations in one step.

a2 + b2 = c2
62 + 82 = 102
36 + 64 = 100
100 = 100

Because both sides of the equations are 100 square units, this triangle is a right triangle. Doubling the length of each side does not change the type of triangle.

   Points to Ponder

Any triangle that has a side ratio of 3:4:5 is a right triangle. This ratio can be used as a shortcut for determining if a corner is square.

Watch this video to see how the 3: 4: 5 ratio for right triangles is used to create a footprint for a backyard project.


The video illustrates the process for constructing square corners. The basic process is:

  • Measure 3 units along one side and mark the 3 unit point (A).
  • Measure 4 units along the second side and mark the 4 unit point (B).
  • Measure between points A and B, they should be exactly 5 units apart. If they are not, make an adjustment until they are exactly 5 units apart.


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