In the parallelogram find: the value of x, total perimeter and area of DEIK?

Answer 1

Perimeter of #DEIK = 14+4sqrt(21) ~~ 32.33 #

Area of #DEIK =12sqrt(21) ~~ 54.99 #

From the diagram:

#EI = 4 = FH#

FGH forms a right angle triangle:

#FH=4, GH=10#

By Pyrthagoroius:

# GH^2=FH^2+FG^2# # :. 100=16+FG^2# # :. FG^2 = 84# # :. FG = 2sqrt(21)#

From the diagram:

# KJ=2x=FG # # :. 2x= 2sqrt(21)# # :. x= sqrt(21)#
To calculate the perimeter of #DEIK#
# P = DE+EI+IJ+JK+DK # # \ \ \ = x+4+x+2x+10 # # \ \ \ = 14+4x # # \ \ \ = 14+4sqrt(21) # # \ \ \ ~~ 32.33 #
To calculate the area of #DEIK#
# A = "Area rect DEIJ" + "Area"triangle DJK # # \ \ \ = DE*EI + 1/2(KJ)(DJ) # # \ \ \ = x*4 + 1/2(2x)(4) # # \ \ \ = 4x + 8x # # \ \ \ = 12x # # \ \ \ = 12sqrt(21) # # \ \ \ ~~ 54.99 #
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Answer 2

To find the value of ( x ) in the parallelogram, we need to use the fact that opposite sides of a parallelogram are equal in length. Since ( DE = 8x ) and ( IK = 3x + 4 ), we can set them equal to each other:

[ 8x = 3x + 4 ]

Solving for ( x ):

[ 8x - 3x = 4 ]

[ 5x = 4 ]

[ x = \frac{4}{5} ]

Now that we have found ( x ), we can use it to find the lengths of the sides and then calculate the perimeter.

The length of ( DE ) is ( 8x = 8 \times \frac{4}{5} = \frac{32}{5} ) units.

The length of ( IK ) is ( 3x + 4 = 3 \times \frac{4}{5} + 4 = \frac{12}{5} + 4 = \frac{12}{5} + \frac{20}{5} = \frac{32}{5} ) units.

So, all sides of the parallelogram are equal to ( \frac{32}{5} ) units.

The perimeter of the parallelogram is the sum of the lengths of all its sides, which is ( 4 \times \frac{32}{5} = \frac{128}{5} ) units.

To find the area of the parallelogram, we can use the formula for the area of a parallelogram, which is the product of its base and height. Since ( DE = \frac{32}{5} ) and ( IK = \frac{32}{5} ), the base and height are the same length.

The area of the parallelogram is ( \frac{32}{5} \times \frac{32}{5} = \frac{1024}{25} ) square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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