Problem:
The area of trapezoid ABCD is 164cm2. The altitude is 8cm,AB is 10cm, and CD is 17cm. What is BC, in centimeters?
Answer Choices:
A. 9
B. 10
C. 12
D. 15
E. 20
Solution:
Label the feet of the altitudes from B and C as E and F respectively. Considering right triangles AEB and DFC,AE=102−82​=36​=6cm, and FD=172−82​=225​=15cm. So the area of △AEB is 21​(6)(8)=24cm2, and the area of △DFC is (21​)(15)(8)=60cm2. Rectangle BCFE has area 164−(24+60)=80cm2. Because BE=CF=8cm, it follows that BC=10cm.
OR
Let BC=EF=x. From the first solution we know that AE=6 and FD=15. Therefore, AD=x+21, and the area of the trapezoid ABCD is (8){21​[x+(x+21)]}=164. So
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