If sin theta > 0 and tan theta < 0 then:
a. 180degree < theta < 270degree
b. 0degree < theta < 90degree
c. 90degree < theta < 180degree
d. 270degree < theta < 360degree

Explanation:

The sign of the trigonometric functions are related with the quadrant on which the terminal sideof the angle lays.

You can use the unit circle to find such relation:

Quadrant    Angle measure       y-coordinate       x-coordinate

                              θ                       sen θ                     cos θ            tan θ

I                        0 < θ < 90°           positive                 positive         positive

II                       90° < θ < 180°      positive                 negative        negative

III                      180° < θ < 270°    negative                negative        positive

IV                     270° < θ < 360°    negative               positive         negative

sin θ > 0 (positive) and tan θ < 0 (negative) is the condition described in the second row of the previous table, then it is the quadrant II and 90° < θ < 180°, which is the option c.

the perimeter is increased by a factor of 2