6)
If two angles have the same measure, the triangle is isosceles. If it is isosceles, it has two sides with the same measure, and a different side (which is the base). This means that the triangle is either a 15-15-20 triangle, or a 15-20-20 triangle. The largest value for the perimeter comes from the second case.
7)
In order to solve this exercise, you have to remind that, in every triangle, the sum of two sides must exceed the third one. So, for example, the first triplet can't represent the sides of a triangle, because the sum of 6 and 7 is 13, which doesn't exceed 14. Repeat this logic for the other triplets to find out which triplets can represent the sides of a triangle.
8)
Consider the point where the height you've drawn meets the base. This point cuts the base in half (because the triangle is isosceles). So, you have two right triangle, where the hypotenuse is the side with length 5, and the legs are the height and half the base. Using the Pythagorean theorem, you can work out the height. From there, you'll easily find the area as half the product of the base (which you know to be 8) and the height (which you will have just found).
9)
If the square has an area of 4, it has a side of 2. The triangle sitting on top of the square is equilateral, so all of its sides have a length of 2 as well. Repeat the same logic of exercise 8 (draw the height and consider the right triangle to find the height) to find the area of the triangle.
