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Kobotan [32]
3 years ago
15

An equilateral triangle has a height of 52 cm. Determine the length of

Mathematics
2 answers:
denis-greek [22]3 years ago
6 0

Answer:

60.04\ cm

Step-by-step explanation:

Let

a ----> the length of each side

we know that

Applying the Pythagorean Theorem

a^2=h^2+(a/2)^2

solve for a

a^2-(a/2)^2=h^2

(3/4)a^2=h^2

a^2=(4/3)h^2

a^2=(4/3)(52)^2

a=60.04\ cm

Dima020 [189]3 years ago
3 0

Answer:

60.04 cm

Step-by-step explanation:

Let the sides of the equilateral triangle be x\: cm

The equilateral triangle has a height of 52 cm.

From the diagram in the attachment, we can apply the Pythagoras Theorem to obtain:

x^2=52^2+(\frac{x}{2})^2

This implies that:

x^2=52^2+\frac{x^2}{4}

We multiply through by 4 to get:

4x^2=10816+x^2

Group similar terms to get:

4x^2- x^2=10816

3x^2=10816

x^2=3605.333

Take square root to get:

x=\sqrt{3605.333}

x=60.04

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