Question

How far from the base of a pyramid of altitude 10m is a section parallel to the base and equal in area to half of the base?

Answer 1

@perl

Answer 2

Because of similarity
A1 / A2 = (L1 / L2 )^2

Answer 3

that was a generic pyramid, you dont need to use that specific pyramid

Answer 4

$$
\Large {
\frac{A_1}{A_2} = \left (\frac{L_1}{L_2} \right)^2
\\ \therefore \\
\frac{A_1}{\frac12 A_1} = \left (\frac{10}{L_2} \right)^2

}
$$

Answer 5

note that you can cancel A_1

Answer 6

volume of pyramid is 1/3Bh Vw/Vp = (hw/hp)^3???

Answer 7

$$
\Large {
\frac{A_1}{A_2} = \left (\frac{L_1}{L_2} \right)^2
\\ \therefore \\
\frac{A_1}{\frac12 A_1} = \left (\frac{10}{L_2} \right)^2
\\ \therefore \\
\frac{\cancel{A_1}}{\frac12 \cancel{A_1}} = \left (\frac{10}{L_2} \right)^2

\\ \therefore \\
\frac{1}{\frac12 } = \left (\frac{10}{L_2} \right)^2
\\ \therefore \\
2 = \left (\frac{10}{L_2} \right)^2

\\ \therefore \\
2 = \frac{10^2}{L_2~^2}
\\ \therefore \\
{L_2~^2} = \frac{10^2}{2}

\\ \therefore \\
L_2 = \sqrt {\frac{10^2}{2 }}

}
$$

Answer 8

5sqrt of 2