An isosceles triangle with base 10 and sides 13. What is the total length of the red line segments?

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## Solution

The total length is 120/13, which is approximately 9,23.

First, the height of the triangle is easily found by the Pythagorean theorem: h=√(13^{2}-5^{2})=12. Therefore its area is 10*12/2=60.

Next, acknowledge that triangle ABC is the union of triangles ADC and BDC, the heights of which are a and b respectively and which both have base 13. Their total area is (a+b)*13/2. Equating this with 60 gives the desired result.

## Visual solution

## Poem

Ricochet

Skip stones in a triangle

Are playing and jumping

From one side to the other

From one angle to one corner

Flat stones into the river throwing

The pebble is surfing

On the water stone skimming

A wave ballet dancing

Wonderfull nature is doing