Answer:
x = 8
Explanation:
We start with the formulas for the area of a rectangle and the area of a triangle.
area of rectangle = length × width
area of triangle = base × height / 2
We want the areas to be equal, so we set the expressions of the areas equal to each other.
length × width = base × height / 2
Now we look in the figure, and we find the given values for:
rectangle length = x + 6
rectangle width = 7
triangle base = 14
triangle height = 2x - 2
Now we go back to the line with the equal expressions, and we substitute in all the given lengths.
length × width = base × height / 2
(x + 6)(7) = 14(2x - 2)/2
(x + 6)(7) = 7(2x - 2)
x + 6 = 2x - 2
-x = -8
x = 8