Question

There is polygon JKLM. It is divided into two triangles, triangle JKM and triangle LKM with a common base KM. The length of side KM is 12, side LM is 9. The measure angle KJM is 60⁰, the measure angle JKM is 60⁰. The angle KML and angle KLM are congruent. What is the perimeter of JKLM?

a) 33
b) 36
c) 39
d) 42

Answer 1

The perimeter of polygon JKLM is calculated by adding up the lengths of all its sides. Triangle JKM is equilateral and triangle LKM is isosceles, which allows us to conclude that the perimeter is 42 units.

Step-by-step explanation:

The question revolves around finding the perimeter of a polygon named JKLM, which is divided into two triangles: JKM and LKM. Given that the side KM equals 12, LM equals 9, angle KJM is 60°, and angle JKM is 60°, we can infer that triangle JKM is an equilateral triangle (all sides are equal because all angles are 60°). Thus, sides JK and JM are each 12 units long.

Additionally, angles KML and KLM are congruent, which makes triangle LKM isosceles with KM and ML being equal in length - 12 and 9 respectively. To find the perimeter of JKLM, we simply add the lengths of all sides: JK + KM + ML + LJ. Since KM is shared by both triangles, its length is counted once, so the perimeter is JK (12) + KM (12) + ML (9) + LJ (9) = 42 units.