Question

Consider kite FGHJ. Kite F G H J is shown. Angle F and H are congruent. The length of side F G is 30 centimeters, the length of side G H is (2 a minus 4) centimeters, the length of H J is 24 centimeters, and the length of F J is (3 b + 6) centimeters. What are the values of a and b? a = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8

Answer 1

a = 17, b = 6

Explanation:

Sides GF and GH are congruent, so we have ...

GF = GH

30 = 2a -4 . . . . substitute given values

15 = a -2 . . . . . divide by 2

17 = a . . . . . . . . add 2

Sides FJ and HJ are congruent, so we have ...

FJ = HJ

3b +6 = 24 . . . . substitute given values

b +2 = 8 . . . . . . divide by 3

b = 6 . . . . . . . . . subtract 2

The values of a and b are (a, b) = (17, 6).