THE BASE OF A TRIANGLE IS 3CM LONGER THAN ITS CORRESPONDING HEIGHT. IFTHE AREA IS 44CM^2. FIND THE LENGTH OF ITS BASE
h(h+3)/2=44
8cm
I don't think this is the right answer
To find the length of the base of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Given that the base is 3 cm longer than the corresponding height, we can represent the length of the height as 'x' cm. Therefore, the length of the base would be 'x + 3' cm.
We are also given that the area is 44 cm^2. Substituting these values into the formula, we get:
44 = (1/2) * (x + 3) * x
Now we can solve this equation to find the length of the base 'x + 3'.
Multiplying both sides by 2 to eliminate the fraction, we have:
88 = (x + 3) * x
Expanding the equation, we get:
88 = x^2 + 3x
Rearranging the equation, we have:
x^2 + 3x - 88 = 0
Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Factoring gives us:
(x + 11)(x - 8) = 0
Setting each factor equal to zero, we have:
x + 11 = 0 or x - 8 = 0
Solving these equations gives us:
x = -11 or x = 8
Since the length cannot be negative, we can discard the solution x = -11.
Therefore, the length of the height is 8 cm.
Substituting this value back into the expression for the base, we get:
Base = x + 3 = 8 + 3 = 11 cm
Therefore, the length of the base of the triangle is 11 cm.
A
1/2(h+3)h