Question

a rectangle abcd which measures 9 ft by 12ft. it folded once perpendicular to diagonal AC such that the opposite vertices A and C coincide. find the length of the fold.

can someone illustrate and answer this?

Answer 1

25 ft

Answer 2

can you illustrate it?

Answer 3

By Pythagorean Theorem, the length of AC is
\[(2x)^2 = 12^2 + 9^2\]
\[4x^2 = 225\]
\[x^2 = \frac{ 225 }{ 4 }\]
\[x = 7.5\]

\[\tan \theta = \frac{ 9 }{ 12 } = \frac{ y }{ x }\]
\[\frac{ 9 }{ 12 }=\frac{ y }{ 7.5 }\]
\[y = \frac{ 9(7.5) }{ 12 }\]
\[y = 5.625\]
\[2y = 2(5.625)\]
\[y = 11.25\]