# Can you answer these math questions?

http://img136.imageshack.us/img136/6083/mathsp4.jp...

If you can, also provide how you got the answer. I need to know these to continue to play NCAA CU football! :-O

### 1 Answer

- MathematicaLv 71 decade agoFavorite Answer
#1:

Since ABM is isosceles, that means AM = AB

also in BMN, then BM = BN

A median cuts the side into two equal halves.

So...

AE = EB

AD = DM

and since AB = AM, then

AE = EB = AD = DM

Same for the other triangle

BP = PM = BC = CN

Also, in an isosceles triangle, the medians from the base angles are congruent. So...

BD = ME

and

NP = MC

So.... Using substitution:

AE + ME + MC + BC = 32

AE = AD

ME = BD

MC = NP

and

BC = BP

So...

AD + BD + BP + NP = 32

**********

#2:

ABN is equilateral, which means each of its angles is 60 degrees (and all three sides are equal length).

AM is a median, which means NM = MB.

Since NM = MB, AN = AB, and angle ANB = angle ABN = 60 degrees, then

triangle ANM is congruent to triangle ABM (by the side-angle-side theorem)

Because they are congruent, then corresponding parts of the triangles are congruent, which means

angle ANM = angle ABM

since angle NAB = 60 degrees (definition of equilateral triangle), and NAB = NAM + MAB

then NAB = MAB = 30 degrees.

Triangle AME is equilateral (given). So

angle AME = angle MEA = angle EAM = 60 degrees

since we know angle MAB = 30 degrees (from above),

and MAE = MAB + BAE

then BAE = 30 degrees.

Since we know AM = AE (equilateral triangle)

and AC = AC (reflexive property),

and angle MAC = angle CAE = 30

by side-angle-side, we again know that

triangle AMC is congruent to triangle AEC

Because corresponding parts of triangles are congruent, we know that MC = CE

Since MC = CE, then AC must be the median of triangle AME.

**********

#3:

We know ABM is equilateral, that means all angles of that triangle are 60 degrees. So, angle AMB is 60 degrees.

Since BME are collinear (make a straight line), then you can find angle AMC.

AMC + AMB + CME = 180

AMC + 60 + 30 = 180

AMC = 90 degrees.

You can use trigonometry on triangle ACM (since it's a right triangle) to find AM.

sin (angle ACM) = (AM) / (AC)

sin 30 = AM / 36

1/2 = AM / 36

18 inches = AM

Source(s): Sorry, I don't know how to do #4.