### Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

### Isosceles

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.

### Linkage

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?

# Isosceles Triangles

##### Age 11 to 14 Challenge Level:

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.