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# Isosceles Triangles

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Age 11 to 14

Challenge Level

*Isosceles Triangles printable sheet*

This question is about isosceles triangles with an area of 9 cm$^2$.

One of the vertices must be at the point (20, 20).

Each vertex of the triangle must be at a grid point of a square grid, so all the vertices will have whole number coordinates.

**How many different triangles satisfy these four conditions?**

Try to find them all. You may wish to use the GeoGebra applet below.

**Can you explain how you know that you have found them all?
**

Click here for a poster of this problem.

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?