Question

The prom committee is decorating the venue for prom and wants for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5, EF=39, and m angle GHF=128 degrees, find GE

Answer 1

Applying the definition of the diagonals of a rectangle, GE = 89 ft.

Diagonals of a Rectangle

• A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other.
• The diagonals of a rectangle bisects each other into equal segments.

The diagonals of the rectangular room are:

DF and GE

• Thus:

DF = GE

DH = 1/2(DF)

• Substitute

44.5 = 1/2(DF)

DF = 2(44.5)

DF = 89

• Therefore:

DF = GE = 89

GE = 89 ft.

Thus, applying the definition of the diagonals of a rectangle, GE = 89 ft.

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