Answer:
1. ACB, CDB and ADC are all similar to eachother.
2. 10
3. CD=8, AD=10.666667, AC=13.33333
4. X=2.4
5. X=√10
6. X=√15
Explanation:
1. To prove triangles are similar, prove they share at least two angles.
Triangle ACB is similar to triangle CDB because they both share a 90° angle and ∠B.
Triangle ACB is similar to triangle ADC because they both share a 90° angle and ∠A.
Since ACB is similar to both CDB and ADC respectively, CDB is similar to ADC.
2. Use similar triangles to find AB
ACB is similar to CDB
AB/CB=CB/DB
AB/10=10/6
AB=100/6=16.666667
Geometric mean: √(16.66667*6)=10
3.
Find CD using Pythagorus:
10²=6²+CD²
CD²=100-36
CD=√64=8
Use similar triangle ratios to find AD:
CDB is similar to ADC.
CD/DB=AD/DC
8/6=AD/8
AD=8(8/6)=10.6666666667
Find AC using Pythagorus:
AC²=10.66666666667²+8²
AC=√177.7777777778
AC=13.333333333
4. √(40²+30²)=50
30/50=X/40
X=2.4
5. (√35)²=X²+5²
35=X²+25
X=√10
6. √((√10)²-(√6)²=√(10-6)=2
√6/2=X/√10
6/4=X²/10
X²=10(1.5)
X=√15