the length of segment ef is 12 cm. which statements regarding triangle def are correct? select three…

the length of segment ef is 12 cm. which statements regarding triangle def are correct? select three options. ef is the longest side of △def. df = 6 cm de = 12√3 cm df = 4√3 cm de = 6√3 cm

the length of segment ef is 12 cm. which statements regarding triangle def are correct? select three options. ef is the longest side of △def. df = 6 cm de = 12√3 cm df = 4√3 cm de = 6√3 cm

Answer

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratios

In a 30 - 60 - 90 triangle, if the hypotenuse (c) is the side opposite the 90 - degree angle, the side opposite the 30 - degree angle (a) and the side opposite the 60 - degree angle (b) have the ratios (a:b:c = 1:\sqrt{3}:2). Here, (EF) is the hypotenuse ((c = 12) cm) since it is opposite the right - angle (\angle D) in (\triangle DEF).

Step2: Find the length of the side opposite the 30 - degree angle

The side opposite the 30 - degree angle ((\angle E)) is (DF). Using the ratio (a=\frac{c}{2}), since (c = 12) cm, then (DF=\frac{12}{2}=6) cm.

Step3: Find the length of the side opposite the 60 - degree angle

The side opposite the 60 - degree angle ((\angle F)) is (DE). Using the ratio (b = a\sqrt{3}), and since (a = DF = 6) cm, then (DE=6\sqrt{3}) cm. Also, the hypotenuse (EF) is the longest side of a right - triangle.

Answer:

  • (\overline{EF}) is the longest side of (\triangle DEF).
  • (DF = 6) cm
  • (DE = 6\sqrt{3}) cm