Question

What is the length of AC? B 7.5 10 A 6.5 D C

Answer 1

Answer: 11.34

Step-by-Step Explanation:

We are given 2 Right Triangles. In the Triangles, as we see, AC = AD + DC.
So, we have to find the measure of AD and DC respectively using Pythagoras Theorem and then add both the measures to get AC.

In Triangle BAD,
AB = 7.5
BD = 6.5
AD = Unknown

Therefore,
AB^2 = BD^2 + AD^2
(7.5)^2 = (6.5)^2 + AD^2
56.25 = 42.25 + AD^2
AD^2 = 56.25 - 42.25
AD^2 = 14
=> AD = √14 = 3.74

In Triangle BDC,
BD = 6.5
BC = 10
DC = Unknown

Therefore,
BC^2 = BD^2 + DC^2
(10)^2 = (6.5)^2 + DC^2
100 = 42.25 + DC^2
DC^2 = 100 - 42.25
DC^2 = 57.75
=> DC = √57.75 = 7.6

Therefore,
AC = AD + DC
AC = 3.74 + 7.6
=> AC = 11.34

Since Options are not provided, please select the option that is closest to this Answer.