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