Answer:
Explanation:
The hypotenuse, opposite side and adjacent side of a right angle triangle are related by the Pythagoras theorem which states that
Hypotenuse ^2 = opposite^2 + adjacent ^2
The hypotenuse of an isosceles right triangle is 2 feet longer than either of its legs. Let x represent the length of the hypotenuse. Then
Either of the other sides is x - 2.
Applying Pythagoras theorem
x^2 = (x - 2)^2 + (x - 2)^2
x^2 = x^2 - 2x - 2x + 4 + x^2 - 2x - 2x + 4
x^2 = x^2 + x^2 - 4x - 4x+ 4 + 4
x^2 = 2x^2 - 8x+ 4 + 4
2x^2 - x^2 - 8x + 8 = 0
x^2 - 8x + 8 = 0
For quadratic formular,
x = -b ±√b^2 - 4ac]/2a
a = 1
b = -8
c = 8
x = [- - 8±√-8^2 - 4× ×1×8]/2×1
x = [8 ±5.66]/2
x = 8 + 5.66]/2 or x = (8 - 5.66)/2
x = 13.66/2 or x = 2.34/2
x = 6.83 or x = 1.17
The hypotenuse is 6.83
Either of the other sides are 6.83 - 2 =4.83