Question

the volume of this triangular prism is 133,000 cubic centimeters. what is the value of g? g = centimeters submit

Explanation:

Step1: Recall the volume formula for a triangular prism.

The volume \( V \) of a triangular prism is given by \( V=\frac{1}{2}\times\text{base}\times\text{height}\times\text{length} \). Here, the base of the triangle can be considered as \( g \), the height of the triangle is \( 35 \) cm, and the length of the prism is \( 100 \) cm. So the formula becomes \( V = \frac{1}{2}\times g\times35\times100 \).

Step2: Substitute the given volume into the formula.

We know that \( V = 133000 \) cubic centimeters. So we have the equation \( 133000=\frac{1}{2}\times g\times35\times100 \). First, simplify the right - hand side: \( \frac{1}{2}\times35\times100=\frac{35\times100}{2}= 35\times50 = 1750 \). So the equation is \( 133000 = 1750\times g \).

Step3: Solve for \( g \).

To find \( g \), we divide both sides of the equation by \( 1750 \). So \( g=\frac{133000}{1750} \). Calculate \( \frac{133000}{1750}=\frac{133000\div50}{1750\div50}=\frac{2660}{35}=\frac{2660\div35}{35\div35}=76 \).

Answer:

\( 76 \)