Final answer:
To find the base of the triangle, set up an equation using the given information. Then solve the equation to find the value of x, which represents the base of the triangle. The base of the triangle is 1 + √31 cm.
Step-by-step explanation:
To find the base of the triangle, we need to set up an equation using the given information. Let's assume the base of the triangle is x cm. According to the given information, the altitude is 2 cm shorter than the base, so the altitude can be expressed as (x - 2) cm.
The formula for the area of a triangle is 1/2 × base × altitude. We are given that the area is 15 cm². Hence, we can set up the equation:
1/2 × x × (x - 2) = 15
Simplifying the equation, we get:
x² - 2x = 30
Bringing all the terms to one side:
x² - 2x - 30 = 0
Now, we can solve this quadratic equation to find the value of x.
Using the quadratic formula, x = (-(-2) ± √((-2)² - 4(1)(-30))) / (2(1))
Simplifying further, x = (2 ± √(4 + 120)) / 2
x = (2 ± √124) / 2
x = (2 ± 2√31) / 2
Crossing out the common factors, we have:
x = 1 ± √31
Since the base of the triangle cannot be negative, we take the positive value:
x = 1 + √31
Therefore, the base of the triangle is 1 + √31 cm.