The altitude drawn to the base of an isosceles triangle is , and the perimeter . The area of the triangle is:
Pick one
Solution
Consider the half of the triangle that is left of the altitude. Using the information given in the problem, we can determine that this is a right triangle with one leg of length 8 whose other two sides sum to 16. Through either setting the other leg as and the hypotenuse as and using the Pythagorean Theorem, or by recognizing this triangle, we find that the other leg has length 6. So the triangle's total area is 48, and our answer is .
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.