Question

Parallelogram EFGH is a rectangle. HE = 6, and FE = 8.

Find GE:

and Find FJ:

Answer 1

GE = 10 and FJ =5

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 =
`(1)/(2)FH`(In a rectangle diagonals bisects equally) = 10÷2 = 5

Answer 2

GE = 10 units,

FJ = 5 units.

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,

`EF^2+EH^2=FH^2,\\ \\8^2+6^2=FH^2,\\ \\FH^2=64+36=100,\\ \\FH=10\ units.`

The diagonals of the rectangle are congruent, so

GE = FH = 10 units.

The diagonals of the rectangle biect each other, thus

`FJ=(1)/(2)FH=(1)/(2)\cdot 10=5\ units.`