Answer:
C
Step-by-step explanation:
Step 1: find BC
Given Triangles ABC and ADE are similar,
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]
BC = [tex]\frac{AB}{AD}[/tex] x DE
= [tex]\frac{8}{8 + 4}[/tex] x 9
= 6 cm
Step 2: use Pythagorean theorem to find AC and / or AE
Consider triangle ABC,
by Pythagorean theorem,
AB² + BC² = AC²
AC² = 6² + 8² = 100
AC = √100 = 10 (answer... we can see that C is the only one with AC=10.
Step 3: Verify.. even though we know that it is C because AC = 10, you can verify that the ansewer is correct by finding CE and confirming that CE=5
By using similar triangles ABC and ADE,
AC/AE = AB / AD
AE = AD/AB x AC = 12/8 x 10 = 15
CE = AE - AC = 15 - 10 = 5 (answer confirmed)
