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Nat2105 [25]
2 years ago
8

In a triangle the base is 4/7 the height and their sum is 110cm. A square is 7/8 of the triangle. Calculate the perimeter of the

square​
Mathematics
2 answers:
rusak2 [61]2 years ago
8 0

Answer:

  • 60 cm

Step-by-step explanation:

Let the height is x, the the base is 4/7x.

<u>Their sum is 110 cm:</u>

  • x + 4/7x = 110
  • 11/7x = 110
  • x = 70

<u>The base is:</u>

  • 110 - 70 = 40 cm

<u>The area of the triangle is:</u>

  • A = 1/2bh = 1/2*70*40 = 1400 cm²

<u>Area of the square:</u>

  • 1400*7/8 = 1225 cm²

<u>Side of the square:</u>

  • √1225 = 15 cm

<u>Perimeter of the square:</u>

  • 15 cm * 4 = 60 cm
Likurg_2 [28]2 years ago
3 0

Perimeter is the continuous line forming the boundary of a closed geometric figure.The formula to find perimeter is (length+width)x2

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stepan [7]

Answer : The correct options are:

DE + EF > DF

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Δ DEF is a scalene triangle.

Step-by-step explanation :

As we know that there are three types of triangle.

(1) Equilateral triangle : It is a triangle in which the three sides and angle are equal.

(2) Isosceles triangle : It is a triangle in which the two sides and two angle are equal.

(3) Scalene triangle : It is a triangle in which the three sides and angle are not equal.

Now we have to determine the length DF.

using Pythagoras theorem:

(Hypotenus)^2=(Perpendicular)^2+(Base)^2

(9)^2=(Perpendicular)^2+(4)^2

81=(Perpendicular)^2+16

(Perpendicular)^2=81-16

(Perpendicular)^2=65

Perpendicular=8.06

The length DF = 8.06 unit

So, we can say that:

DE + EF > DF

Hence, from the given options we conclude that, the correct options are:

DE + EF > DF

5 < DF < 13

Δ DEF is a scalene triangle.

8 0
3 years ago
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Write a rule for the nth term of the sequence.
Helga [31]

Answer:

The rule for given sequence is: a_n = -27+16n

And the 100th term is: 1573

Step-by-step explanation:

Given sequence is:

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a_1 = -11\\a_2 = 5\\a_3 = 21\\a_4 = 37

First of all, we have to find if this is an arithmetic sequence

For that purpose, the common difference has to be found. Common difference, denoted by d, is the difference between consecutive terms of an arithmetic sequence

So,

d = a_2 -a_1 = 5-(-11) = 5+11 = 16\\d = a_3 -a_2 = 21-5 = 16\\d = a_4-a_3 = 37-21 = 16

As the common difference is same, the sequence is an arithmetic sequence

General rule for arithmetic sequence is:

a_n = a_1+(n-1)d

Putting values

a_n = -11+(n-1)(16)\\a_n = -11+16n-16\\a_n = -27+16n

For 100th term,

Putting n=100

a_{100} = -27+16(100)\\a_{100} = -27+1600 = 1573

Hence,

The rule for given sequence is: a_n = -27+16n

And the 100th term is: 1573

6 0
3 years ago
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RSB [31]

Step-by-step explanation:

(5x + 7) { }^{2}  = 25 {x}^{2}  + 2(5)(7) + (49)

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8 0
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serg [7]

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The average rate of change between these input values is

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6 0
3 years ago
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