Question

Look at the square pyramid in the image with the given measurements determine the length of the base of the square pyramid so the middle is 20 M eyes and then the outer slant is 25

Answer 1

To determine the length of the base of a square pyramid given the height from the base to the apex and the slant height, we can use the following method:

1. **Understand the dimensions**:
- Let \( h \) be the height of the pyramid (20 m from the base to the apex).
- Let \( l \) be the slant height (25 m).
- Let \( a \) be the length of the base of the square pyramid.

2. **Use the relationship**:
In a right triangle formed by the height (\( h \)), half the base length (\( \frac{a}{2} \)), and the slant height (\( l \)), we can apply the Pythagorean theorem:

\[
l^2 = h^2 + \left(\frac{a}{2}\right)^2
\]

3. **Substitute the known values**:
- \( l = 25 \, \text{m} \)
- \( h = 20 \, \text{m} \)

Plugging in the values, we get:

\[
25^2 = 20^2 + \left(\frac{a}{2}\right)^2
\]

Thus:

\[
625 = 400 + \left(\frac{a}{2}\right)^2
\]

4. **Solve for \( \frac{a}{2} \)**:

\[
625 - 400 = \left(\frac{a}{2}\right)^2
\]

\[
225 = \left(\frac{a}{2}\right)^2
\]

Taking the square root of both sides gives:

\[
\frac{a}{2} = 15
\]

5. **Calculate the base length \( a \)**:

\[
a = 2 \times 15 = 30 \, \text{m}
\]

Therefore, the length of the base of the square pyramid is **30 meters**.