Final answer:
The height of the triangle is 4 cm and the base is 8 cm.
Step-by-step explanation:
In this problem, we are given that the triangle is 4 cm wider than it is tall, and the area is 16 cm2. Let's denote the height of the triangle as x cm. We can then write the base of the triangle as (x + 4) cm.
Using the formula for the area of a triangle: A = 1/2 * base * height, we can substitute in the known values: 16 = 1/2 * (x + 4) * x.
Simplifying the equation: 16 = 1/2 * (x2 + 4x).
Multiplying both sides by 2: 32 = x2 + 4x.
Combining like terms and rearranging the equation: x2 + 4x - 32 = 0.
Factoring the quadratic equation: (x - 4)(x + 8) = 0.
This gives us two possible solutions: x = 4 cm or x = -8 cm. Since we cannot have a negative height, the height of the triangle is 4 cm. The base of the triangle is (4 + 4) cm = 8 cm.