What is the perimeter, in cm, of quadrilateral ABCD if $\overline{AB} \perp \overline{BC}$, $\overline{DC} \perp \overline{BC}$, AB=9 cm, DC=5 cm, and BC=12 cm?
+128474 \( $\overline{AB} \perp \overline{BC}$, $\overline{DC} \perp \overline{BC}$,\)
AB = 9 DC = 5 BC = 12
We have trapezoid
D 5 C
12
A E B
9
Let DE be perpendicular to AB
And DE = BC = 12 And AE = AB - DC = 9 - 5 = 4
ADE forms a right triangle
By the P Theorem
AD = sqrt [ DE^2 + AE^2 ] = sqrt [ 12^2 - 4^2 ] = sqrt [ 144 - 16] = sqrt (128) = 8sqrt (2)
The perimieter = 5 + 12 + 9 + 8sqrt (2) = 26 + 8sqrt (2) cm
