The strength of a beam varies inversely with the square of its length. If a 15-foot beam can support 500 pounds, how many pounds can a 20-foot beam support?
A) 261.15
B)279.33
C)281.25
D)732.50
what is 500(15/20)^2
To solve this problem, we can use the inverse square variation formula:
Strength1 / Strength2 = (Length2^2) / (Length1^2)
Let's calculate the strength of the 20-foot beam using the given information:
Length1 = 15 feet
Strength1 = 500 pounds
Length2 = 20 feet
Strength2 = (Strength1 * (Length2^2)) / (Length1^2)
Strength2 = (500 * (20^2)) / (15^2)
Strength2 = (500 * 400) / 225
Strength2 = 200000 / 225
Strength2 = 888.88 pounds (approx.)
Therefore, a 20-foot beam can support approximately 888.88 pounds.
None of the provided answer choices matches our result.
To solve this problem, we can set up a proportion using the inverse square relationship between the strength of the beam and its length.
Let's represent the strength of the beam as S and the length of the beam as L. According to the problem, we know that the strength of the beam varies inversely with the square of its length, meaning:
S ∝ 1/L^2
Now, let's set up a proportion using the given data. We are given that a 15-foot beam can support 500 pounds. So we have the ratio:
S1/L1^2 = S2/L2^2
Substituting the given values, we have:
500/15^2 = S2/20^2
Solving for S2, we can cross multiply and solve for S2:
500 * 20^2 = S2 * 15^2
Now, we can calculate the value of S2:
S2 = (500 * 20^2) / 15^2
Simplifying the calculations:
S2 = (500 * 400) / 225
S2 = 200000 / 225
S2 ≈ 888.89
Therefore, a 20-foot beam can support approximately 888.89 pounds.
None of the listed answer choices match this result. It is possible that there was a mistake in the calculations or the options provided are incorrect.