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3 years ago

What is the side of equilateral triangle is altitude is 10

Mathematics

1 answer:

kotegsom [21]3 years ago

5 0

Answer:

11.55

Step-by-step explanation:

An equilateral triangle is one which all it sides are equal.

10cm altitude means the height is 10cm.

Using Pythagoras theorem,

x² = 10² + (x/2)²

Assume that the side of the triangle is xcm

x² - x²/4 = 100

3x²/4 = 100

x = √(400/3)

x = 11.55cm

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A) Find the value of N if, Kn has 105 edges.

blagie [28]

The number of edges can be calculated from the number of vertices.

There are 14 vertices for 105 edges
There are 200 vertices for 19900 edges

The variable N is used to always represent the number of vertices.

So, we represent the edges as:

$E \to Edges$

(a) The value of N for 105 edges

The relationship between N and E is:

$E = \frac{N \times (N - 1)}{2}$

Substitute 105 for E

$105 = \frac{N \times (N - 1)}{2}$

Multiply through by 2

$210 = N \times (N - 1)$

$210 = N^2 - N$

Rewrite as:

$N^2 - N - 210 = 0$

Expand

$N^2 +14N - 15N - 210 = 0$

Factorize

$N(N +14) - 15(N + 14) = 0$

Factor out N + 14

$(N - 15) (N + 14) = 0$

Solve for N

$N = 15$ or $N = -14$

The number of vertices (N) cannot be negative. So:

$N = 15$

(b) The value of N for 19900 edges

We have:

$E = \frac{N \times (N - 1)}{2}$

Substitute 19900 for E

$19900 = \frac{N \times (N - 1)}{2}$

Multiply through by 2

$39800 = N \times (N - 1)$

$39800= N^2 - N$

Rewrite as:

$N^2 - N - 39800= 0$

Expand

$N^2 +199N - 200N - 39800= 0$

Factorize

$N(N +199) - 200(N + 199) = 0$

Factor out N + 199

$(N + 199) (N - 200) = 0$

Solve for N

$N = 200$ or $N = -199$

The number of vertices (N) cannot be negative. So:

$N = 200$

Hence, there are 200 vertices for 19900 edges

Read more about vertices and edges at:

brainly.com/question/22118318

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