Answer:
The dimensions of the right triangle are 9 meters by 7 meters.
or
The base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base).
Explanation:
To find the dimensions of the right triangle, we can use the formula for the area of a triangle, which is:
A = 1/2 * b * h
Where b is the base and h is the height of the triangle. In this case, we know that the area of the triangle is 40 square meters, and the height is 2 meters less than the base, so we can write the equation as:
40 = 1/2 * b * (b - 2)
To solve for b, we can rearrange the equation to get b by itself:
40 = 1/2 * b^2 - b
Then, we can move all the terms involving b to the left-hand side of the equation and all the constants to the right-hand side:
1/2 * b^2 - b - 40 = 0
Next, we can use the quadratic formula to solve for b:
b = (-(-1) +/- sqrt((-1)^2 - 4 * (1/2) * -40)) / (2 * (1/2))
Which simplifies to:
b = (1 +/- sqrt(1 + 80)) / 1
Since b must be a positive number, we take the positive solution:
b = (1 + sqrt(81)) / 1
Therefore, the base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base). Thus, the dimensions of the right triangle are 9 meters by 7 meters.