Hypotenuse word problem

The two legs of a right triangle are the same length. The hypotenuse is 4 meters long.

Find the length of the legs. Express your answer in simplified radical form, or as a decimal rounded to four places.

Solution

Let x be the length of one leg and let x be the length of the other leg.

x2 + x2 = 42

2x2 = 16

Divide both sides by 2

x2 = 8

x = √(8)

x = √(4 × 2)

x = √(4) × √(2)

x = 2 × √(2)

or

x = 2 × 1.414213

x = 2.828426

x = 2.8284

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