Question

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

Answer 1

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

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

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

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

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

$a=60.04\ cm$

Answer 2

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:

$x=\sqrt{3605.333}$

$x=60.04$