Question

The strength of a rectangular beam varies

directly as the square of it depth. If the strength
of a beam 10 inches deep is 3600 pounds per
square inch, what is the strength of a beam four
six inches deep?

Answer 1

• 1296 pounds per square inch

Explanation:

Direct variation equation:

• y = kx

In this case it is:

• y = kx², where y- strength, x- depth of the beam, k- coefficient

Substitute the given values and solve for k:

• 3600 = k*10²
• 3600 = 100k
• k = 3600/100
• k = 36

The equation becomes:

• y = 36x²

Now, find the value of y, when x is 6:

• y = 36*6² = 1296

Note, I took the depth as 6 inches but the question is a bit confusing by saying "four six inches". If it is 4 inches then your answer will be:

• y = 36*4² = 576