Question

a civil engineer relates the thickness t, in inches, and height h, in feet, of a square wooden pillar to its crushing load l, in tons, using the model t = 4/25 * √(lh²). if a square wooden pillar is 6 inches thick and 10 feet high, what is its crushing load? (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Identify given values

$T = 6$, $H=10$

Step2: Substitute into formula

We use the formula $T=\frac{4}{25}\cdot\frac{L}{H^{2}}$. Substituting $T = 6$ and $H = 10$ into it, we get $6=\frac{4}{25}\cdot\frac{L}{10^{2}}$.

Step3: Solve for L

First, simplify the right - hand side: $\frac{4}{25}\cdot\frac{L}{100}=\frac{4L}{2500}=\frac{L}{625}$. So the equation becomes $6=\frac{L}{625}$. Cross - multiply to find $L=6\times625 = 3750$.

Answer:

3750