Answer:
60.04 cm
Step-by-step explanation:
Let the sides of the equilateral triangle be [tex]x\: cm[/tex]
The equilateral triangle has a height of 52 cm.
From the diagram in the attachment, we can apply the Pythagoras Theorem to obtain:
[tex]x^2=52^2+(\frac{x}{2})^2[/tex]
This implies that:
[tex]x^2=52^2+\frac{x^2}{4}[/tex]
We multiply through by 4 to get:
[tex]4x^2=10816+x^2[/tex]
Group similar terms to get:
[tex]4x^2- x^2=10816[/tex]
[tex]3x^2=10816[/tex]
[tex]x^2=3605.333[/tex]
Take square root to get:
[tex]x=\sqrt{3605.333}[/tex]
[tex]x=60.04[/tex]
