In ∆abc, the median am (m ∈ bc ) is perpendicular to the angle bisector bk (k ∈ ac ). find ab, if bc = 12 in.

The answer is 6 inches

Step-by-step explanation:

Since the angle is isosceles, angle A and angle B have the same measure, 

The sum of the angles of any triangle is 180°.

So 2 times the measure of angle B plus  120° = 180°, then the equation:

Solving for x we get: 

Now we use the law of sine on the triangle BMC like this:

Solving for BC we get : 

We apply the law of sin again on the isosceles triangle ABC like this:

Solving for AB we get:

6 inches

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.