Respuesta :

frika

Answer:

GE = 10 units,

FJ = 5 units.

Step-by-step explanation:

A rectangle is a parallelogram with all interior angles of 90°. Since angle E has the measure 90°, then the triangle EFH is right triangle. By the Pythagorean theorem,

[tex]EF^2+EH^2=FH^2,\\ \\8^2+6^2=FH^2,\\ \\FH^2=64+36=100,\\ \\FH=10\ units.[/tex]

The diagonals of the rectangle are congruent, so

GE = FH = 10 units.

The diagonals of the rectangle biect each other, thus

[tex]FJ=\dfrac{1}{2}FH=\dfrac{1}{2}\cdot 10=5\ units.[/tex]

Answer:

GE = 10 and FJ =5

Step-by-step explanation:

Since parallelogram is a rectangle therefore opposite sides of the rectangle will be equal and all angles of the rectangle will be 90°.In addition to this diagonals of the rectangle bisects each other in equal parts.

Given side HE = 6 and Side FE = 8

Therefore from ΔEGH side GE = √GH²+HE²(By Pythagoras Theorem)

GE = √6²+8²=√36+64 = √100 = 10

Since GE = FH ( diagonals of rectangle are equal)

Therefore FJ = [tex]\frac{1}{2}FH[/tex](In a rectangle diagonals bisects equally) =  10÷2 = 5


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