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

   Constructing Knowledge

People who work in construction-related careers often need to make sure that the work they are doing is square (meaning 90° angles are formed). People who frame walls often use geometric techniques to check if the walls are square. If walls are framed incorrectly, and are not square, the next steps, such as laying flooring or putting drywall on the ceiling, become more difficult.

A 3:4:5 technique is commonly used in construction when making sure walls are square. To determine if walls are square, workers measure lengths on perpendicular walls before the walls are secured into place. They will measure 3 feet down one wall, 4 feet along the other wall and then make sure these two spots are exactly 5 feet apart. If they are not, an adjustment will be made, and then the walls will be secured in place.

EXAMPLE 1

Is a triangle that has leg lengths of 3 and 4 and a longest side of 5 a right triangle?

Solution


Step 1: Draw and label the diagram.



Step 2: Calculate the square of the longest side.

The longest side is 5 units long

c2 = 52
= 25 square units

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

The other two sides are 3 and 4

a2 + b2 = 32 + 42
= 9 + 16
= 25 square units

Because both side of the equations are 25 square units, this triangle is a right triangle.

Alternate Solution


You can also do these calculations in one step.

a2 + b2 = c2
32 + 42 = 52
9 + 16 = 25
25 = 25

Because both side of the equations are 25 square units, this triangle is a right triangle.


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