A construction company needs to build thirty trusses for the roof of a house.
The truss is 20 ft long on the top two sides.
What is the bottom length of the truss?
the options for this answer were:
a)30ft
b)40ft
c)50ft
d)60ft
When I solved this, I got 28.3
missing information.
Did you forget an angle or something like that?
no
in the problem?
the diagram of the truss had 6 triangles inside it with a pentagon in the middle
I sqrt 20 and got 400
400+400 = 800 sqrt
it said which is an acceptable length for the bottom
Still not enough. There are too many possibilities.
Are the triangles congruent, equilateral or are some angles given?
Is the pentagon touching the base?
Does the pentagon fit into the top of the truss?
etc ??
To find the bottom length of the truss, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the truss that are 20 ft long each represent the "legs" of the right triangle, and the bottom length represents the "hypotenuse." Let's call the bottom length "x."
So, applying the Pythagorean theorem, we have:
(20 ft)^2 + (20 ft)^2 = x^2
Simplifying the equation, we get:
400 ft^2 + 400 ft^2 = x^2
800 ft^2 = x^2
To find x, we take the square root of both sides:
√(800 ft^2) = √(x^2)
√(800 ft^2) = x
Calculating the square root of 800 ft^2, we get:
x ≈ 28.3 ft
So, the bottom length of the truss is approximately 28.3 ft.
Given the provided options, the closest length to 28.3 ft is 30 ft, so the correct option would be (a) 30 ft.