Question

Given: ΔABC, AC = BC, AB = 3 CD ⊥ AB, CD = √3 Find: AC

Answer 1

Answer:

$\boxed{AC = 2.3}$

Step-by-step explanation:

AD = BD  (CD bisects AB means that it divides the line into two equal parts)

So,

AD = BD = AB/2

So,

AD = 3/2

AD = 1.5

Now, Finding AC using Pythagorean Theorem:

$c^2 = a^2+b^2$

Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)

$AC^2= (1.5)^2+(\sqrt{3} )^2$

$AC^2 = 2.25 + 3$

$AC^2 = 5.25$

Taking sqrt on both sides

$AC = 2.3$

Answer 2

Answer:

$\boxed{2.29}$

Step-by-step explanation:

The length of AB is 3 units.

The length of CD is $\sqrt{3}$ units.

D is the mid-point of points A and B.

AD is half of AB.

$\frac{3}{2} =1.5$

Apply Pythagorean theorem to solve for length of AC.

$c=\sqrt{a^2 +b^2 }$

The hypotenuse is length AC.

$c=\sqrt{1.5^2 +(\sqrt{3}) ^2 }$

$c=\sqrt{2.25+3 }$

$c=\sqrt{5.25}$

$c= 2.291288...$