Question

Use the image to answer the question.

A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.

The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
ft.

Answer 1

To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem, which relates the height (h), the slant height (l), and the half-length of the edge of the base (b).

Given:

- Height (h) = 321 ft
- Slant height (l) = 436.5 ft

The relationship can be expressed as:

\[ l^2 = h^2 + b^2 \]

We need to solve for \( b \). First, we will plug in the values:

\[
(436.5)^2 = (321)^2 + b^2
\]

Calculating the squares:

\[
436.5^2 = 190,663.25
\]

\[
321^2 = 103,041
\]

Now we substitute these values back into the equation:

\[
190,663.25 = 103,041 + b^2
\]

Next, isolate \( b^2 \):

\[
b^2 = 190,663.25 - 103,041
\]

\[
b^2 = 87,622.25
\]

Now we take the square root to find \( b \):

\[
b = \sqrt{87,622.25} \approx 296.0 \text{ feet}
\]

Since \( b \) represents half the edge length of the square base, the full edge length \( L \) will be:

\[
L = 2b = 2 \times 296.0 \approx 592.0 \text{ feet}
\]

Thus, the length of the edge of the square base, rounded to the nearest tenth, is:

**592.0 ft.**