Final answer:
To find the height of the trapezoid, we can set up a system of equations using the perimeter and area formulas. By solving this system, we can find the value of the height. In this case, the height of the trapezoid is approximately 2.25 cm.
Step-by-step explanation:
To find the height of the trapezoid, we first need to find the length of its bases. Let's say the shorter base is 'a' and the longer base is 'b'. The perimeter of a trapezoid is given by the formula P = a + b + 2h, where h is the height. Since the perimeter is given as 50 cm, we can write the equation as 50 = a + b + 2h.
The area of a trapezoid is given by the formula A = 1/2 (a + b)h. Since the area is given as 90 cm², we can write the equation as 90 = 1/2 (a + b)h.
Now we have a system of equations with two unknowns (a and b) and one variable (h). We can solve this system to find the value of h.
Let's first eliminate a. From the perimeter equation, we have a = 50 - b - 2h. Substituting this into the area equation, we get 90 = 1/2 (50 - b - 2h + b)h.
Simplifying the equation, we have 180 = 50h - h². Rearranging it to a quadratic equation, we get h² - 50h + 180 = 0.
Solving this quadratic equation, we find that h ≈ 2.25 cm. Therefore, the correct answer is A) 2.25.