Find the base length of a triangle that has an area of 5454 cm2 and height 33 cm more than its base length.

To find the base length of the triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height.

Given that the area of the triangle is 5454 cm^2 and the height is 33 cm more than the base length, we can set up the following equation:

5454 = 1/2 * base * (base + 33)

Multiplying both sides by 2 to get rid of the fraction gives:

10908 = base * (base + 33)

This is a quadratic equation in the form of ax^2 + bx + c = 0, where x is the base length, a is 1, b is 33, and c is -10908.

We can solve this equation using the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Substituting the values gives:

base = [-33 ± sqrt((33)^2 - 41(-10908))] / (2*1) base = [-33 ± sqrt(1089 + 43632)] / 2 base = [-33 ± sqrt(44721)] / 2 base = [-33 ± 211] / 2

This gives two possible solutions: base = 89 cm or base = -122 cm.

Since the base length of a triangle cannot be negative, the base length of the triangle is 89 cm.