An isosceles triangle has a base with length x+4 and the other two sides have length x+3. The perimeter of this isosceles triangle is 16cm. Find the area of the triangle.
First, we need to find the value of x. The perimeter of a shape is the sum of the length of all of its sides, so the perimeter of this isosceles is x + 4 + 2(x + 3) = x + 4 + 2x + 6 = 3x +10. We are told that the perimeter is equal to 16, so setting the equation equal to 16 gives 3x + 10 = 16, meaning that 3x = 6 and so x = 2. Therefore, the base has length x + 4 = 2 + 4 = 6, and the other sides have length x + 3 = 2 + 3 = 5.Now that we know what the actual lengths of each side are, we need to calculate the area. Area of a triangle = 1/2 x base x height. We know that the base = 6, but don't know the height yet. To find the height, we can split our isosceles into two identical right angled triangles whose hypotenuse (the side opposite to the right angle) has length 5 and the base has length 1/2 x 6 = 3. By Pythagoras' Theorem, 52 = 3 2 + height2, therefore height2 = 16 and so height = 4. Substituting the height and base into the formula for area gives us: Area of triangle = 1/2 x 6 x 4 = 12.
