Given right triangle ABCABC with altitude \overline{BD}

BD

drawn to hypotenuse ACAC. If AC=12AC=12 and DC=4,DC=4, what is the length of \overline{BC}

BC

in simplest radical form?

The correct answer is 4√3

Step-by-step explanation:

Consider the triangle ABC.

BC = 12 units. ∠ B = 90°. Let ∠ C = α°.

Now let us consider the triangle BDC.

DC = 4 units. ∠ D = 90°. Let ∠ C = α°.

We find here the angle C is common between both the triangles.

∴ For ΔABC, cos α° = =

and for Δ BDC, cos α° =

Now equating both the equations we get,

= 48

⇒ BC = 4√3

The length of BC is 4√3 units.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal

6: 00am, ok,6 plus 11 gives you 5: 00 am and 45 plus 15 gives you 60.00 mins plus 5: 00 am gives you 6: 00 am;

step-by-step explanation: