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Intermediate

The ricochet

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.

Solution by M.S.Sivakumar.

First, the height of the triangle is easily found by the Pythagorean theorem: h=√(132-52)=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

Visual solution by David Andriana.

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

Bella

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