Question

To store his art supplies, Kyle buys a cube-shapped box with 8-inches sides. His longest paintbrush is 13.5 inches long. Explain how kyle determined that the 13.5 inch brush could fit in the box. (Show mathematical, explain in words, solve mathematically and draw diagram)

Answer 1

Kyle should calculare diagonal (3D)of that box because its the longest segment in the box.
First we want to find diagonal of the base, so
diagonal of base is from Pythagorean theorem, so
$8^2+8^2=d^2$
$d^2=128$
$d=8 \sqrt{2}$
Now we can use again P theorem but with the triangle with sides, diagonal of the base, height it box and 3D diagonal.
So we have
$(8 \sqrt{2} )^2+8^2=(d3D)^2$
$(d3D)^2=192 d3D=8 \sqrt{3} d3D=13.85$ so its more that paintbrush