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Problem about equilateral triangles

Nich6ls

New member
May 30, 2021
4
Hi! I need help with this exercise: A side of one equilateral triangle equals the height of a second equilateral triangle. Find the ratio of the perimeter of the larger triangle to that of the smaller. A "detailed solution" to be analysed by me then.

Answer: \[ 2/3 sqrt3 \]

Thanks
 

Euge

MHB Global Moderator
Staff member
Jun 20, 2014
1,925
Use the fact that triangles are similar. If $x$ represents the side of first triangle, show that the triangle's height is $x\frac{\sqrt{3}}{2}$. The second triangle has height $x$, and since the triangles are similar, the ratio of their perimeters is equal to the ratio of their heights. Conclude.