The area of a triangle is 45cm and the altitude is 5cm greater than the base. Find the length of the base.
base --- b
height = b+5
(1/2)(b)(b+5) = 45
b^2 + 5b = 90
b^2 + 5b - 90 = 0
b = (-5 ±√385)/2
= appr 7.311 or some negative
base = 7.311 , height = 12.311
check
area = (1/2)(7.311)(12.311) = 45.0028..
not bad, my answer is correct
To find the length of the base of the triangle, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the area is 45 cm and the altitude (or height) is 5 cm greater than the base, we can set up the following equation:
45 = (base * (base + 5)) / 2
To solve for the base, we can multiply both sides of the equation by 2:
90 = base * (base + 5)
Expanding the equation:
90 = base^2 + 5base
Rearranging the equation into a quadratic form:
base^2 + 5base - 90 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use factoring. We need to find two numbers whose product is -90 and sum is 5.
The numbers that satisfy these conditions are -10 and 9. Therefore, we can rewrite the equation as:
(base - 10)(base + 9) = 0
Setting each factor to zero and solving for the base:
base - 10 = 0 --> base = 10
base + 9 = 0 --> base = -9
Since we cannot have a negative base in a triangle, the base of the triangle is 10 cm.