find the area of the triangle whose base is:
2a+2b
_______
a-b
and the height is:
a-b
_______
a^2 + 3ab + 2b^2
Thank you!!
To find the area of the triangle, we can use the formula:
Area = (1/2) * base * height
Given:
Base = 2a+2b
Height = (a-b) / (a^2 + 3ab + 2b^2)
Now we can substitute the values into the formula to calculate the area:
Area = (1/2) * (2a+2b) * ((a-b) / (a^2 + 3ab + 2b^2))
Next, we can simplify the expression:
Area = (a+ b) * ((a-b) / (a^2 + 3ab + 2b^2))
To further simplify the expression, we can distribute a and b to the terms inside the parentheses:
Area = (a^2 - ab + ab - b^2) / (a^2 + 3ab + 2b^2)
The terms -ab and ab cancel out, leaving:
Area = (a^2 - b^2) / (a^2 + 3ab + 2b^2)
Therefore, the area of the triangle is (a^2 - b^2) / (a^2 + 3ab + 2b^2).