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Masja [62]
3 years ago
11

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

Mathematics
2 answers:
Luda [366]3 years ago
5 0

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...

valina [46]3 years ago
3 0

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

<u><em>Now, Finding AC using Pythagorean Theorem:</em></u>

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

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