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slava [35]
3 years ago
9

The ratio of the lengths of the sides of a triangle ABC is 3:4:6. M, N, and K are the midpoints of the sides. Perimeter of the △

MNK equals 5.2 in. Find the length of the sides of the △ABC. No picture.
Mathematics
1 answer:
juin [17]3 years ago
7 0

Given that in a trianlgle the sides AB, BC, CA are in the ratio 3:4:6.

Let AB = 3k, BC = 4k and CA = 6k.

Then perimeter =3k+4k+6k = 13k

M, N, K are mid points of the sides.

By mid point theorem MN = 3k/2, NK = 4k/2 and KM = 6k/2

Hence perimeter of MNK = 13k/2 =5.2 (given)

Solve for k

k=2(5.2)/13 = 0.8

Hence sides are

AB = 3k = 3(0.8) = 2.4 in

BC = 4k= 3.2 in

CA = 4.8 in

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Use decimals and fractions in the same equation showing the Commutative Property. Repeat for the Associative Property.
Anna71 [15]

For Commutative Property of Addition

Let us take a decimal number 2.14 and a fraction \frac{5}{20}

Now, according to the Commutative property of Addition:

For any two numbers a and b :

a+b = b+a

So, for 2.14 and \frac{5}{20}

Let us add

2.14+\frac{5}{20}  = \frac{214}{100}  +\frac{5}{20}

                                   =\frac{214}{100}  + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100}  + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39

Also,

\frac{5}{20} + 2.14  = \frac{5}{20} + \frac{214}{100}

                                     = \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100}  + \frac{214}{100} \\ \\=  0.25 + 2.14 \\ \\ = 2.39

Therefore, 2.14+\frac{5}{20} = \frac{5}{20} + 2.14

Hence,  Commutative Property of Addition is satisfied.


For Associated Property of Addition

Let us take two same decimal numbers 2.14 , 7.25 and a fraction \frac{5}{20}

Now, according to the Associated property of Addition:

For any three numbers a, b  and  c

a + (b+c) =(a+b) + c

So, for 2.14 , 7.25 and \frac{5}{20}

The Left hand side:

a + (b+c)

2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})

                                                         = 2.14 + (\frac{725}{100} + \frac{25 }{100})

                                                         = 2.14 + (\frac{750}{100} )

                                                        = \frac{214}{100} + \frac{750}{100}

                                                         = \frac{964}{100}

                                                        =9.64


The Right hand side:

(a + b )+c

(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}

                                                = 9.39  + \frac{5 \times 5 }{20 \times 5}

                                                = 9.39  + \frac{25}{100}

                                                = 9.39  + 0.25

                                                = 9.64


Thus,

(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}

Therefore, 2.14+\frac{5}{20} = \frac{5}{20} + 2.14

Hence,  Associative Property of Addition is satisfied.




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HELP ME PLZZ I NEED HELP WITH THIS!!
VARVARA [1.3K]

Answer:

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Step-by-step explanation:

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