Determine the maximum area of a triangle in square centimetres, if the sum of its base and its height is 10 cm. 1.) The sum of the

## Step 1: Expressing height in terms of base### Let 'b' be the base and 'h' be the height of the triangle. We are given that . We can express the height in terms of the base: .## Step 2: Area of the triangle### The area of a triangle is given by the formula . Substituting , we get .## Step 3: Finding the maximum area### To find the maximum area, we can complete the square or find the vertex of the parabola represented by the area function. The x-coordinate of the vertex of a parabola in the form is given by . In our case, , so and . Thus, . Substituting into the area formula: .