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BARSIC [14]
3 years ago
12

The length of a rectangle is 4n centimeters, and it is twice as long as the width. The perimeter of the rectangle is twice as lo

ng as that of an equilateral triangle. Find the side length of the triangle in terms of n.
PLEASE HELP AND SHOW WORK
Mathematics
1 answer:
sladkih [1.3K]3 years ago
6 0
4n  -  t<span>he length of a rectangle
4n : 2 = 2n  -  </span>the width of a rectangle

P = (4n + 2n) * 2
P = 12n 

12n : 2 = 6n - the perimeter of the equilateral triangle
P = 3a
6n = 3a
a = 6n : 3
a = 2n - <span>the side length of the triangle - answer.</span>
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Solve the proportions:
IRINA_888 [86]

<u>Answer:</u>

  • 6. 6.75
  • 7. 27
  • 8. 92/17
  • 9. 49

<u>Step-by-step explanation:</u>

<u>- Question 6 -</u>

  • 9/16 = x/12
  • => 16x = 12 x 9
  • => 16x = 108
  • => x = 6.75

Hence, <u>the value of x in this proportion is 6.75.</u>

<h3>_______________________________</h3>

<u>- Question 7 -</u>

  • -3 + x/18 = 12/9
  • => -3/18 + x/18 = 4/3
  • => x/18 = 4/3 + 1/6
  • => x/18 = 8/6 + 1/6
  • => x/18 = 9/6
  • => x = 9/6 x 18
  • => x = 27

Hence, <u>the value of x is 27</u>

<h3>_______________________________</h3>

<u>- Question 8 -</u>

17/15 = 10/2x - 2

=> 17(2x - 2) = 150

=> 34x - 34 = 150

=> 34x = 184

=> x = 184/34

=> x = 92/17

Hence, <u>the value of x is 92/17</u>

<h3>_______________________________</h3>

<u>- Question 9 -</u>

  • x - 16/x + 6 = 3/5
  • => 5(x - 16) = 3(x + 6)
  • => 5x - 80 = 3x + 18
  • => 2x = 98
  • => x = 49

Hence, <u>the value of x is 49.</u>

<h3>_______________________________</h3>

Hoped this helped.

3 0
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