The hypotenuse of an isosceles right triangle is 2 feet longer than either of its legs. find the exact length of each side. use the quadratic formula to find your answer.

Step-by-step 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

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