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MrRa [10]
3 years ago
6

The hypotenuse of a right triangle is 15cm long. One of the triangle’s legs is two times the length of the other leg. Find the l

engths of the three sides of the triangle
Mathematics
2 answers:
Slav-nsk [51]3 years ago
7 0

Answer:

15, 3\sqrt{5} and 6\sqrt{5}

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let one leg be x then the other leg is 2x, then

x² + (2x)² = 15², that is

x² + 4x² = 225

5x² = 225 ( divide both sides by 5 )

x² = 45 ( take the square root of both sides )

x = \sqrt{45} = \sqrt{9(5)} = 3\sqrt{5}

The other leg is 2 × 3\sqrt{5} = 6\sqrt{5}

vladimir2022 [97]3 years ago
6 0

Answer:

6.7cm, 13.4cm, 15cm.

Step-by-step explanation:

Let x be one side of the triangle. The question tells us the other side is 2x.

We can relate all 3 sides using the Pythagorean Theorem:

15^2=x^2+(2x)^2\\225=x^2+4x^2\\225=5x^2\\x^2=45\\x=6.7

That means the side lengths are 6.7cm and 2 x 6.7 cm = 13.4cm.

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