Question

IF <I is congruent to <K, find the perimeter of <JIK.

A. 14
B. 16
C. 21
D. 23

Answer 1

The correct answer option is D. 23.

Explanation:

We know that the angle I and angle K are congruent. It means that triangle JIK is an isosceles triangle and so the sides opposing these two angles will be same i.e. side KJ and side IJ.

KJ = IJ where KJ = 9x - 11 and IJ = 6x - 5.

So putting these values equal to each other to find the value of x:

9x - 11 = 6x - 5

9x - 6x = 11 - 5

3x = 6

x = 2

Now that we know x = 2, we can find the perimeter of JIK.

Perimeter of JIK = (7x-5) + (9x-11) + (6x-5)

= 7x + 9x + 6x - 5 - 11 - 5

= 22x - 21

= 22 (2) - 21

= 23

Answer 2

Answer: Option D. 23

Solution:

If <I is congruent to <K, this is an isosceles triangle, and two of the sides must be congruent too (the opposite sides to the congruent angles), then:

Side oposite to <I must be congruent to side opposite to <K

KJ=IJ

Replacing KJ by 9x-11 and IJ by 6x-5:

9x-11=6x-5

Solving for x: Subtracting 6x and adding 11 both sides of the equation:

9x-11-6x+11=6x-5-6x+11

3x=6

Dividing both sides of the equation by 3:

3x/3=6/3

x=2

With x=2 we can find the length of the three sides:

KJ=9x-11

KJ=9(2)-11

KJ=18-11

KJ=7

IJ=6x-5

IJ=6(2)-5

IJ=12-5

IJ=7

KI=7x-5

KI=7(2)-5

KI=14-5

KI=9

Then, the perimeter of triangle JIK (P) is:

P=KJ+IJ+KI

P=7+7+9

P=23