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Semmy [17]
3 years ago
10

In Triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.

Mathematics
1 answer:
Roman55 [17]3 years ago
5 0

The perimeter of triangle ABC is 24 units

Step-by-step explanation:

If a segment joining the mid points of two sides of a triangle, then

this segment is:

  • Parallel to the third side
  • Its length is half the length of the third side

In The triangle XYZ

∵ A is the mid point of XY

∵ B is the mid point of YZ

∴ AB = \frac{1}{2} XZ

∵ XZ = 18 units

- Substitute the value of XZ in AB

∴ AB = \frac{1}{2} × 18 = 9 units

∵ B is the mid point of YZ

∵ C is the mid point of XZ

∴ BC = \frac{1}{2} XY

∵ AY = 7 units

∵ AY = \frac{1}{2} XY

∴ XY = 2 × AY

∴ XY = 2 × 7

∴ XY = 14 units

∴ BC = \frac{1}{2} × 14 = 7 units

∵ A is the mid point of XY

∵ C is the mid point of XZ

∴ AC = \frac{1}{2} YZ

∵ BZ = 8 units

∵ BZ = \frac{1}{2} YZ

∴ YZ = 2 × BZ

∴ YZ = 2 × 8

∴ YZ = 16 units

∴ AC = \frac{1}{2} × 16 = 8 units

∵ The perimeter of a triangle = the sum of the lengths of its sides

∴ Perimeter Δ ABC = AB + BC + AC

∴ Perimeter Δ ABC = 9 + 7 + 8 = 24 units

The perimeter of triangle ABC is 24 units

Learn more:

You can learn more about triangles in brainly.com/question/5924921

#LearnwithBrainly

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The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x
mars1129 [50]

We can use the equation x=\frac{3}{4} y to find the length of the side of a square.

<u>Solution:</u>

Given that, the perimeter of a square is equal to the perimeter of an equilateral triangle.  

The length of a side of the square is given by "x"

And the length of a side of the equilateral triangle is given by "y"

Finding the equation to determine value of "x"

<em><u>The perimeter of a square with side "x" is given as:</u></em>

\text { perimeter of a square }=4 \times \text { side }=4 x

<em><u>Perimeter of a equilateral triangle with side "y" is given as:</u></em>

\text { perimeter of a equilateral triangle }=3 \text { side }=3 y

Given that perimeter of a square = perimeter of an equilateral triangle

\begin{array}{l}{\rightarrow 4 x=3 y} \\\\ {\rightarrow x=\frac{3}{4} y}\end{array}

Hence, we can use the equation x=\frac{3}{4} y to find the length of the side of a square.

3 0
3 years ago
how many ways can we award a 1st, 2nd, and 3rd place prize among eight contestants? A) 336 B.) 56 C.) none of these D.) 40320​
alekssr [168]

the answer is A.336

Explanation:

There are 8 choices for awarding first prize.Then there are 7 choices for awarding second prize.And there are 6 choices for awarding third prize.

Therefore, there are: 8 *7 *6 =336 ways.

4 0
3 years ago
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In order to clear out room for new merchandise, James decided to mark down some of the items for sale in his electronics store.
masya89 [10]

The correct answer is A, as the DVD player's price was reduced by $ 3.82 more than the stereo tuner's price.

In order to clear out room for new merchandise, James decided to mark down some of the items for sale in his electronics store, and he marked down DVD players by 36%, and he marked down stereo tuners by 22%, if DVD Players cost $ 41.60 after the markdown and stereo tuners cost $ 69.42 after the markdown.

To determine which item's price was reduced by more, and by how many dollars more was it reduced, the following calculation must be performed:

  • 100 - 36 = 64
  • 64 = 41.60
  • 100 = X
  • 100 x 41.60 / 64 = X
  • 4160/64 = X
  • 65 = X
  • 65 - 41.60 = 23.40

  • 100 - 22 = 78
  • 78 = 69.42
  • 100 = X
  • 69.42 x 100/78 = X
  • 6942/78 = X
  • 89 = X
  • 89 - 69.42 = 19.58

Therefore, the DVD player's price was reduced by $ 3.82 more than the stereo tuner's price.

Learn more about maths in brainly.com/question/18629331

4 0
2 years ago
What is the length of a rectangle with a width of 10 cm and area of 120 cm???
melamori03 [73]

Answer:

12cm

Step-by-step explanation:

Width = 10 cm

Area = 120 cm²

Length = ?

Area = Length(L) × Width(W)

120cm²  = L × 10cm

L = 120cm² ÷ 10 cm = 12cm

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Choose the imensions that represen this rectlangl
almond37 [142]

Answer:B

Step-by-step explanation:I hope it help

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