Answer
BC = x = 3√10
Explanation
To answer this question, we will use the concept of similar triangles.
We know that the two triangles ABC and BDC are similar because they are right angle triangles with one common non-right angle angle too, Angle C.
Using angle C as a reference point, we can write the corresponding sides.
And we know that corresponding sides for similar triangles have the same ratio.
∆ABC = ∆BDC
AB is corresponding to BD
BC is corresponding to DC
CA is corresponding to CB
So,
(AB/BD) = (BC/DC) = (CA/CB)
The sides that we need include
BC, DC, CA and CB
BC = x
DC = 6
CA = 15
CB = x
(BC/DC) = (CA/CB)
(x/6) = (15/x)
Cross multiply
x² = (6)(15)
x² = 90
Take the square root of both sides
√(x²) = √(90)
x = √90
x = √[(9)(10)]
x = (√9) (√10)
x = 3√10
Hope this Helps!!!
