A triangle has sides 20 cm, 21 cm and 29 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A triangle has sides cm, cm and cm. Show that it is right-angled. Then find how many right triangles with whole-number sides have a hypotenuse of or less.
Need a reminder? The key ideaShow
Pythagoras theorem: in a right triangle with the right angle at B, . The converse: if , the angle at B is a right angle. To find a hypotenuse, add the squares of the legs. To find a leg, subtract the square of the known leg from the square of the hypotenuse.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The squares. .
Step 2. The longest side. . The two are equal, so by the converse the triangle is right-angled, with the right angle opposite the cm side.
Step 3. Count the triples. Try every hypotenuse up to and every pair of shorter sides. The program finds triples: , , , , , , , , , and .
Answer: it is right-angled, and there are such triangles.
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