Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Question #a86ed

1 Answer

Jul 26, 2016

See explanation.

Explanation:

If we assume that the side of the triangle is $a$ $a$ then we can write that:

$A L = \frac{a \sqrt{3}}{2}$ $AL=(asqrt(3))/2$ - $A L$ $AL$ is a height in an equilateral triangle.
$C L = B L = \frac{a}{2}$ $CL=BL=a/2$ because $A L$ $AL$ is also the bisector of the triangle's side $B C$ $BC$

so $A L^{2} = \frac{3}{4} a$ $AL^2=3/4a$ and $B L^{2} = \frac{a^{2}}{4}$ $BL^2=a^2/4$ , so $A L^{2} = 3 B L^{2}$ $AL^2=3BL^2$

QED

Related questions

See all questions in Angles with Triangles and Polygons

Impact of this question

1479 views around the world

You can reuse this answer
Creative Commons License