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atroni [7]
4 years ago
11

Which quadrilaterals have diagonals that are always perpendicular to each other?

Mathematics
2 answers:
lorasvet [3.4K]4 years ago
8 0

Answer:

Rhombus and square

Step-by-step explanation:

The quadrilaterals that satisfy this condition are rhombi and squares.

lilavasa [31]4 years ago
7 0

Answer:

rhombus and square

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Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the sq
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Let the first number of the five we are looking for equal n.

Because the numbers are consecutive, the next four can be expressed as (n+1), (n+2), (n+3) and (n+4).

Our series of 5 numbers is therefore n,(n+1),(n+2),(n+3),(n+4).

We are told the sum of the squares of the first 3 is equal to the sum of the squares of the last 2 therefore:
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expand all the brackets to give
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factorising this gives us
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That means that n,(n+1),(n+2),(n+3),(n+4) could be [-2, -1, 0, 1 and 2] or [10, 11, 12, 13 and 14].

Since the question asks for whole numbers, and negative numbers are not classed as whole numbers, the numbers we want must be 10, 11, 12, 13 and 14.

You can check this on a calculator by doing 10² + 11² + 12² (=365) and 13² + 14² (=365).
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