Look at the diagram below.
Triangle E-D-C with the base side as E-D is inscribed in triangle A-D-B with the base side as A-D have a common vertex D.
If
and AB = 18 inches, AE = 5 inches, and CE = 6 inches, what is the length of
?
A.
B.
2.5 inches
C.
D.
7.5 inches
B. 2.5 inches
To find the length of AD, we can use similar triangles.
Let x be the length of AD.
Using similar triangles AED and CED:
AE/CE = AD/CD
5/6 = x/(18-x)
5(18-x) = 6x
90 - 5x = 6x
90 = 11x
x = 90/11 = 8.18 inches
Therefore, the length of CD is 18 - 8.18 = 9.82 inches.
Now we can find the length of BC:
BC = CD - CE
BC = 9.82 - 6
BC = 3.82 inches
Finally, we can find the length of DE:
DE = AE - CE
DE = 5 - 6
DE = -1 inches
Since DE is negative, it means it doesn't exist in this case. Therefore, the length of is not applicable.