Right Triangle one leg is 400ft. long. The hypotenuse of the triangle is 200ft. longer than the other leg. What is the dimensions of this triangle?
let the other leg be x , where x is in hundred of feet (I am avoiding large numbers)
x^2 + 4^2 = (x+2)^2
x^2 + 16 = x^2 + 4x + 4
4x = 12
x=3 ----> 300 ft
So the sides are 200, 300 and 500
To determine the dimensions of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's assign variables to the dimensions of the triangle:
Let x be the length of one leg of the triangle (which is shorter than the hypotenuse).
Let y be the length of the other leg of the triangle (which is longer than x).
According to the given information, we have:
x = 400 ft (length of one leg)
hypotenuse = y + 200 ft (length of the hypotenuse)
Applying the Pythagorean theorem:
x^2 + y^2 = (y + 200)^2
Expanding the equation:
x^2 + y^2 = y^2 + 400y + 400^2
Simplifying:
400^2 = 400y
40000 = y
Substituting y back into the equation for x:
x^2 + (40000)^2 = (40000 + 200)^2
x^2 + 1600000000 = 40200^2
x^2 + 1600000000 = 16160400
x^2 = 1600000000 - 16160400
x^2 = 1583845600
Taking the square root of both sides:
x = sqrt(1583845600)
x ≈ 39798.05 ft
So, one leg of the triangle is approximately 39798.05 ft long, the other leg is 40000 ft long, and the hypotenuse is 40200 ft long.