In the parallelogram find: the value of x, total perimeter and area of DEIK?
Perimeter of Area of
From the diagram:
FGH forms a right angle triangle:
By Pyrthagoroius:
From the diagram:
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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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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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