Question

5) Unique Building Company is constructing a triangular

roof truss for a building. The workers assemble the truss with
the dimensions shown on the diagram below. Using the Pythagorean
Theorem (a² + b² = c² where c is the side across from the right angle and
a and b are the legs that form the right angle), find the length of all sides of
the truss.

Answer 1

a = 3 yd

b = 4 yd

c = 5 yd

Explanation:

We can use the Pythagorean Theorem to find the value of x as follows:

a² + b² = c²

(x)² + (x+1)² = (2x-1)²

x² + x² + 2x + 1 = 4x² - 4x + 1

2x² - 6x = 0

2x(x-3) = 0

x = 0 or x = 3

Since x cannot be 0, we have x = 3.

Now we can use x=3 to find the lengths of all sides:

a = x = 3 yd

b = x+1 = 4 yd

c = 2x-1 = 5 yd

Therefore, the length of all sides of the truss are:

a = 3 yd

b = 4 yd

c = 5 yd