Question

Quadrilateral JKLM is a kite as such KM is a perpendicular bisector of J L at point P given that KP =4" JL equals 12" and AML equals 20" was the length of the permenter of the quad JKlM?

Answer 1

40 + 4√13

Explanation:

A kite is a quadrilateral (has four sides) with two pairs of equal adjacent sides. The longer diagonal of a kite bisects the shorter diagonal.

Since in kite JKLM, diagonal KM bisects JL, hence KM is the longer diagonal.

JP = LP

JL = 12

JL = JP + LP

12 = JP + LP

2JP = 12 (LP = JP)

JP = 6

We can find JK using Pythagoras theorem, hence:

JK² = JP² + KP²

JK² = 4² + 6²

JK² = 16 + 36

JK² = 52

JK = √52 = 2√13

JK = KL = 2√13

ML = JM = 20

Perimeter of kite = JK + KL + ML + JM = 20 + 20 + 2√13 + 2√13

Perimeter of kite = 40 + 4√13