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At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again? ### 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. 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? As triangle ABC is equilateral, ∠BAC = $60$°. Since the grey triangles are equilateral, ∠ADE = $60$°, so the triangle ADE is equilateral.
The length of the side of this triangle is equal to the length of $DE = (5 + 2 + 5)\;\mathrm{cm} = 12\;\mathrm{cm}$. So $AF = AD - FD = (12 - 5)\;\mathrm{cm} = 7\;\mathrm{cm}$.
By a similar argument, we deduce that $BD = 7\;\mathrm{cm}$, so the length of the side of the triangle $ABC = (7 + 5 + 7)\;\mathrm{cm} = 19\;\mathrm{cm}$.