Question

What is the perimeter of JKLM?

Answer 1

45 units

Explanation:

JkM is an equilateral triangle. JK =12 and JM= 12.

MKL is an isosceles triangle KM = KL. KM = 12

3(12)+9 = 36+9= 45 units

Answer 2

45

Explanation:

The perimeter of a polygon is the sum of its side lengths.

We can see that polygon JKLM is composed of:

• isosceles triangle KLM
• equilateral triangle JKM

Since JKLM is a quadrilateral, it has 4 sides. We are given 1 side length:

• LM = 9

and 1 cross-section length:

• KM = 12

Because JKM is an equilateral triangle, meaning all of its angles are congruent, we know that all of its sides are congruent as well:

• JK = 12
• MJ = 12

We can solve for the length of the final side (KL) using the Isosceles Triangle Theorem, which states that if the base angles of a triangle are congruent, then its legs (the 2 sides other than the base) are also congruent:

• KL = 12

Finally, we can find the perimeter of JKLM by finding the sum of its side lengths:

P = JK + KL + LM + MJ

P = 12 + 12 + 12 + 9

P = 45