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3 years ago

The altitude of an equilateral triangle is 5 cm. what is the length of a side of the triangle?

Mathematics

1 answer:

Grace [21]3 years ago

3 0

Answer:

The length side of the triangle is $\frac{10\sqrt{3}}{3}\ cm$

Step-by-step explanation:

we know that

The equilateral triangle has three equal sides and three equal internal angles of measure of 60 degrees each.

Let

b------> the length side of the equilateral triangle

Applying Pythagoras theorem

$b^{2}=(b/2)^{2}+5^{2}\\\\ b^{2}-(b/2)^{2}=25\\\\ (3/4)b^{2}=25\\ \\b^{2} =25*4/3\\ \\b=\frac{10}{\sqrt{3}}\ cm\\ \\b=\frac{10\sqrt{3}}{3}\ cm$

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lakkis [162]

Answer/Step-by-sep explanation:

1. Given:

∆NMK ≅ ∆TRP

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b. The side that is congruent to $\overline{TR}$ is $\overline{NM}$ . Thus:

$\overline{TR}$ ≅ $\overline{NM}$

c. Since $\overline{TR}$ ≅ $\overline{NM}$ , therefore:

$\overline{TR} = \overline{NM}$

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2. a. Slope of LK = $\frac{rise}{run} = \frac{4}{3}$

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b. ✍️Length of LK is the distance between L(-7, 4) and (-4, 8):

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✍️Length of LM is the distance between L(-7, 4) and (-2, 1):

$LM = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$LM = \sqrt{(-2 -(-7))^2 + (1 - 4)^2}$

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∆KLM is not an isosceles ∆ because it does not has two equal side lengths. This we can see because LK and LM are not equal.

Therefore, Anthony is incorrect. Am isosceles ∆ has two equal sides.

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3 years ago