Question

The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the

lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.

Answer 1

4 feet, 1.4 feet, 4.2 feet

Explanation:

We are looking for the lengths of the three sides of a right triangle. We are given that one leg has length 4ft. Let x be the length of the other leg. Since the hypotenuse of the right triangle is three times the length of this leg, we can represent the hypotenuse as 3x. This is a right triangle, so we can use the Pythagorean Theorem to find x.

42+x216+x2=(3x)2=9x2

Subtracting x2 from both sides, then dividing by 8 to isolate the x, we have

8x2x2x=16=2=±2–√

Considering only the positive value for x, the lengths of the three sides of the triangle are approximately 4 feet, 2–√≈1.4 feet, and 32–√≈4.2 feet.

Answer 2

Explanation:

Let the other leg = x

x^2 + 4^2 = (3x)^2

x^2 + 4^2 = 9x^2

4^2 = 9x^2 - x^2

16= 8x^2

16/8 = x^2

x^2 = 2

x = sqrt(2)

The lengths of the sides

x = sqrt(2)

other side =4

hypotenuse = 3*sqrt(2)

x = 1.4

other side= 4

hypotenuse = 3*1.4142

hypotenuse = 4.2