Children living in the edge read a passage and write title

Answer:

Some plains form as ice and water erodes, or wears away, the dirt and rock on higher land

Detailed Solution

The greatest number of four digit is 9999.

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If adjacent sides of a parallelogram are equal and one of the diagonals is equal to any one of the sides of the parallelogram, then AC : BD = ⎷3 : 1.

step by step explanation:

As ABCD is a parallelogram,

Therefore, AB=CD and BC=AD

Now, according to the question AB=BC,

Therefore, AB=BC=CD=AD

Hence, ABCD is a rhombus.

Now, as one of the diagonals is equal to its sides, therefore, AB=BC=CD=AD=BD

Let's assume AB=BC=CD=AD=BD=a

As, BD=a,

⇒ BO=a/2  (Since, in a rhombus diagonals bisect each other at right angle)

Hence, △AOB is right-angled at O.

Now, apply the Pythagoras theorem on △AOB,

⇒ AB2 = BO2 + AO2

⇒ a2 = (a/2)2 + AO2

⇒ AO2 = a2 - a2/4

⇒ AO2 = 3a2/4

⇒ AO = a⎷3/2

As AO = a⎷3/2, therefore AC = 2AO = a⎷3 units.

Therefore, the length of the diagonals are AC = a⎷3 units and BD = a units.

The ratio of the diagonals is:

AC/BD = a⎷3/a

= ⎷3/1

Therefore, AC : BD = ⎷3 : 1.

Let abcd be a parallelogram

so, AB=CD and BC=AD

Now, according to the question AB=BC,

Therefore, AB=BC=CD=AD

Hence, ABCD is a rhombus. ( when a parallelogram has adjacent sides equal and one diagonal equal then it is a rhombus)

Now, as one of the diagonals is equal to its sides, therefore, AB=BC=CD=AD=BD

Let's assume AB=BC=CD=AD=BD=a

As, BD=a,

⇒ BO=a/2 (Since, in a rhombus diagonals bisect each other at right angle)

Hence, △AOB is right-angled at O.

In triangle aob

⇒ AB2 = BO2 + AO2 (by pythagoras theorem)

⇒ a2 = (a/2)2 + AO2

⇒ AO2 = a2 - a2/4

⇒ AO2 = 3a2/4

⇒ AO = a⎷3/2

As AO = a⎷3/2, therefore AC = 2AO = a⎷3 units.

Therefore, the length of the diagonals are AC = a⎷3 units and BD = a units.

The ratio of the diagonals is:

AC/BD = a⎷3/a

= ⎷3/1

Therefore, AC : BD = ⎷3 : 1.

Hence the diagonals are in ratio √3:1

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The greatest number of four digit is 9999.

LCM of 24, 36 and 54 = 2 × 2 × 2 × 3 × 3 × 3 = 216

The greatest number of four digit which exactly divisible by 24, 36, and 54.

9999 – 63 = 9936

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Answer:

9999

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