11.2
The base of a triangle is eight more than twice its height. If the area of the triangle is 53 square centimeters, find its base and height.

The height of the triangle is $\square \square$ and the base of the triangle is $\square \square$
(Simplify your answers, including any radicals. Use integers or fractions for any numbers in the expressions.)

Step 1 ：The area of a triangle is given by the formula \( \frac{1}{2} \times \text{base} \times \text{height} \).

Step 2 ：We know that the base of the triangle is eight more than twice its height, so we can express the base as \(2h + 8\), where \(h\) is the height of the triangle.

Step 3 ：We can substitute this into the formula for the area of the triangle and set it equal to 53, the given area. This will give us an equation in terms of \(h\), which we can solve to find the height of the triangle.

Step 4 ：Once we have the height, we can substitute it back into the expression for the base to find the base of the triangle.

Step 5 ：The solutions for the height and base of the triangle include both positive and negative values. However, in the context of this problem, it doesn't make sense to have negative values for the height and base of a triangle. Therefore, we discard the negative solutions and take the positive solutions as the height and base of the triangle.

Step 6 ：Final Answer: The height of the triangle is \( \boxed{5.55} \) and the base of the triangle is \( \boxed{19.10} \).