15. What are the lengths of the sides of this equilateral...

15. What are the lengths of the sides of this equilateral triangle? 3x + 6 9x - 12 6x - 3 A. 45 B. 15 C. 10.5 D. 3 16. If PO is an angle bisector of ?MON , find the value of x. (2x - 10) (x + 15) A. 5 B. 25 C. -5 D. -25 Use the figure to the right to answer questions 22 and 23. 17. Name a median. A. KI B. GL C. JM D. HJ

Transcript

00:01 Let's now determine the side lengths of this equated triangle with side lengths given as shown in this equated triangle.

00:08 So in an equated triangle, we know that all the three sides are congruent.

00:13 So therefore, this side with the side length, 3x plus 6 is congruent to this side with the side length 6x minus 3.

00:21 Also congruent to the third side with the side length 9x minus 12.

00:26 So we can write down this equation as 3x.

00:30 Plus 6 equals 6x minus 3 equals 9x minus 12 so now we have to solve for x so i consider one of this as equation or i could also consider the other part as the equation to solve for x so here i'm considering 3x plus 6x equal to 6x minus 3 so first i subtract 6x from both sides so when i do that i get 3x minus 6x plus equals 6x minus 6x minus 3.

01:06 So we can cancel this 6x negative 6x.

01:09 This becomes 0.

01:13 Therefore we have 3x minus 6x is negative 3x plus 6 equals negative 3.

01:22 So we have to solve for x.

01:24 So we subtract 6 from both sides.

01:27 So i'm going to subtract 6 like this.

01:31 And when i do that, i get negative 3x equals negative 9.

01:37 Now i divide both sides by negative 3, so that i solve for x.

01:42 So i divide by negative 3.

01:44 This negative 3 cancels with negative 3 as plus negative 9 cancels with negative 3 as 3 times.

01:52 So we can say that x equal to 3.

01:56 So we have determined the value of x, which means we can substitute in any one of the sides.

02:02 All the three sides are congruent so we plug in the value of x equal to three in one of the sides to determine the side length let me plug in into this one so this is six times of x minus three when i plug in it becomes a six times of three minus three this is equal to six times of three is 18 minus three is 15 so therefore the side length of this equal to triangle is 15 we can in fact verify we plugging in one of the other side suppose if i plug into this side this becomes three times of three plus six this skews three times of three is nine plus six equals 15 so here also the side length is 15 in fact when you plug in into this side length we will also get the side length as 15 so therefore the side length of this equal to triangles 15 and this means choice b is the correct let's now do this question number 16 here we have a triangle n -o -m and in this the segment o p bisects the angle m -o -n so we know from the fact that any angle bisector divides any angle into two congruent angles suppose we have a ray like this and the angle this ray is let's say this is 30 degree and if there is an angle bisector so we draw an angle bisector like this this angle by sector devise this total angle between these rays into two congruent angles that means it divides exactly into two equal parts so we can divide this 30 by 2 and see that this angle is 15 degree as plus this angle is also 15 degree so this is some information about the angle bisector we will replace this concept and solve the value of x...

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