Quinn is a budding fashion designer known for incorporating geometry into her creations. Her newest design is a simple black blouse patterned with same-size right triangles in different funky colors. The longer leg of each right triangle will be twice as long as the shorter leg, and the hypotenuse of each triangle will be 6 inches long.To the nearest tenth of an inch, what will be the length of the shorter leg of each triangle?

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can write this as:

a² + b² = c²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. We know that the hypotenuse is 6 inches (c = 6), and that one leg (let's say a) is half the length of the other leg (b = 2a). We can substitute these values into the equation:

a² + (2a)² = 6²

Solving this equation will give us the length of the shorter leg (a).

a² + 4a² = 36 5a² = 36 a² = 36 / 5 a = sqrt(36 / 5) a = sqrt(7.2) a = 2.7 inches

So, the length of the shorter leg of each triangle will be approximately 2.7 inches.