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maw [93]
3 years ago
9

The diagonals of a rhombus are 16 and 30. What is the perimeter

Mathematics
2 answers:
AnnyKZ [126]3 years ago
7 0

Answer: 68

Step-by-step explanation: Let's start this problem by drawing the picture of the rhombus which I have attached for you in the image provided.

A rhombus is a quadrilateral that has 4 congruent sides and the diagonals of a rhombus are perpendicular to each other. The diagonals of a rhombus bisect each other so the diagonal that has a length of 16 is split into two segments that each have a length of 8. The diagonal that has a length of 30 is split into two segments that each have a length of 15.

Now, remember that we're asked to find the perimeter of the rhombus which is the sum of the lengths of all the sides. Since the four sides of the rhombus are equal in length, we can give all four sides of the rhombus a length of <em>X.</em>

<em />

To find the value of <em>X</em>, notice that we have a right triangle in the upper right of the figure so the pythagorean theorem tells us that (15)² + (8)² = (x)² which simplifies to 225 + 64 = x² or 289 = x².

Now we can square root both sides to get 17 = x.

This means that the length of each side of our rhombus is 17. Remember that we are asked to find the perimeter of the rhombus which is the sum of the lengths of all the sides so the perimeter is 17 + 17 + 17 + 17 or 68.

Therefore, the perimeter of the rhombus is 68.

Varvara68 [4.7K]3 years ago
5 0
The perimeter will be
.. P = 2√(16^2 +30^2) = 2*34 = 68
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Complete the following sentence. The slope of the graph of y = 5 x is ___
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comparing with the slope-intercept form of the line equation

The slope of the line = m = 5

Therefore, we conclude that the slope of the graph of y = 5 x is 5.

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3 0
3 years ago
at a maximum speed, an airolane travels 1680 miles against the windin 5 hours. Flying with the wind, the plane can travel the sa
Licemer1 [7]

Answer:

Plane Speed (x) = 378 mph

Step-by-step explanation:

Equation

d = r * t

Givens

With the wind

  • d = 1680 miles
  • t = 4 hours
  • r = x + y

Against the wind

  • d = 1680
  • t = 5 hours
  • r = x - y

Equation

The distances are the same, so you can solve for x in terms of y and then deal with the actual distance.

(x + y)*4 = (x - y)*5                   Remove the brackets on both sides

Solution

  • 4x + 4y = 5x - 5y                     Subtract 4x from both sides
  • 4y = -4x + 5x - 5y                    Combine
  • 4y = x - 5y                               Add 5y to both sides                      
  • 5y + 4y = x
  • x = 9y

Solution part 2

Now take one of the distance formulas and solve for x first then y.

  • (x - y)*5 = 1680               Substitute 9y for x
  • (9y - y)*5 = 1680             Subtract on the left
  • 8y * 5 = 1680                  Multiply on the left
  • 40y = 1680                     Divide by 40
  • y = 1680/40            
  • y = 42                             That's the speed of the wind.
  • (x - y)*5 = 1680               Substitute the wind speed for y
  • (x - 42)*5 = 1680             Divide both sides by 5
  • (x - 42) = 1680 / 5            Do the division on the right
  • (x - 42) = 336                   Add 42 to both sides.
  • x = 336 + 42
  • x = 378 mph                    Plane's speed

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