Final answer:
Using the area formula for triangles and the given relationship between base and height, we find that the height of the triangle is 9 cm and the base is 17 cm.
Step-by-step explanation:
To solve the problem, we use the area formula for a triangle, which is Area = 1/2 × base × height. We are given that the area is 90 square centimeters and the base exceeds the height by 8 cm. Let's denote the base as b and height as h. Thus, b = h + 8.
Substituting the latter into the area formula, we get:
1/2 × (h + 8) × h = 90
Solving for h, we get two values but dismiss the negative one as it doesn't apply to geometric lengths.
After solving, we find that h = 9 cm and b = 17 cm.