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3 years ago

a rectangle that is 30 inches long and 10 inches wide can be divided into two congruent squares. True or false?

Mathematics

2 answers:

Sever21 [200]3 years ago

8 0

Answer:

False

Step-by-step explanation:

To split the rectangle into 2 parts, you can go one of two ways. One way would make the parts 15" by 10", and the other way would make the two parts 30" by 5". Neither way is equal on all sides, which means neither one is a square. That would make the statement false.

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

| |

| 5 |

| |

| _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|

| 30 |

| |

| 5 |

| |

| _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

| 15 | 15 |

| | |

| | 10 |

| | |

| _ _ _ _ _ _ _ _ _ _ _ _ _ _ | _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |

**Pretend my drawings are accurate to the lines, the tops and bottoms are actually 30 and 10 in measurement :-) **

Hope this helps!

mamaluj [8]3 years ago

6 0

Answer:

I think false

Step-by-step explanation:

That's probably going to lead to 3 congruent squares i think, not the answer you were looking for? Sorry, that's all the evidence i have

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For the given set, first calculate the number of subsets for the set, then calculate the

vodomira [7]

Answer:

$\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}$

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ( $N$ ) of subsets of a set containing $n$ elements: N = $2^{n}$

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = $2^{4} = 16$

(same result as using counting method)

Brief proof of formula: N = $2^{n}$

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are $n$ elements in total. => There are $2^n}$ ways to select, or in other words, there are $2^{n}$ subsets.