Asked by Helen

In ΔABC, AC = BC, CD ⊥ AB with D ∈ AB , AB = 4 in, and CD = square root of 3 in. Find AC.

Answered by Reiny
Clearly ΔABC is isosceles, and CD bisects AB.
So AD = 2, and in ΔADC you now have 2 of the sides given

Use Pythagoras to find the hypotenuse AC
Let me know what you get
Answered by Anonymous
tell us
Answered by lizzerbetty
The answer is the square root of 7.
Answered by anonymous
CB = sqrt 7

Explanation:

First, draw an iso triangle, since AC = BC
it should look like this: ( I did my best)
C
/ | \
/ - | - \
A D B

Since ACB is an iso triangle, and CD is perpendicular to the base, CD will be an angle bisector

so, AD = AB = 1/2 AB
AD = AB = 2

If we use the Pythagorean theorem, we'll get this equation:
(2)^2 + ((sqrt 3))^2 = (CB)^2
If we solve, we get
4+3=CB^2
7=CB^2
sqrt 7 = CB
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