This problem can be solved using 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.

In this case, we can think of Liz's house, Roy's house, and Hazel's house as forming a right triangle. The distance from Liz's house to Hazel's house is one side of the triangle (3 miles), the distance from Liz's house to Roy's house is the other side, and the distance from Roy's house to Hazel's house is the hypotenuse (4 miles).

Let's denote the distance from Liz's house to Roy's house as x. According to the Pythagorean theorem, we have:

x^2 + 3^2 = 4^2

Solving this equation for x gives:

x^2 = 4^2 - 3^2
x^2 = 16 - 9
x^2 = 7

Taking the square root of both sides gives:

x = sqrt(7) ≈ 2.6

So, Liz's house is approximately 2.6 miles from Roy's house.

Question

This problem can be solved using 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.

In this case, we can think of Liz's house, Roy's house, and Hazel's house as forming a right triangle. The distance from Liz's house to Hazel's house is one side of the triangle (3 miles), the distance from Liz's house to Roy's house is the other side, and the distance from Roy's house to Hazel's house is the hypotenuse (4 miles).

Let's denote the distance from Liz's house to Roy's house as x. According to the Pythagorean theorem, we have:

x^2 + 3^2 = 4^2

Solving this equation for x gives:

x^2 = 4^2 - 3^2
x^2 = 16 - 9
x^2 = 7

Taking the square root of both sides gives:

x = sqrt(7) ≈ 2.6

So, Liz's house is approximately 2.6 miles from Roy's house.

Knowee AI · Accepted Answer

This problem can be solved using 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.

In this case, we can think of Liz's house, Roy's house, and Hazel's house as forming a right triangle. The distance from Liz's house to Hazel's house is one side of the triangle (3 miles), the distance from Liz's house to Roy's house is the other side, and the distance from Roy's house to Hazel's house is the hypotenuse (4 miles).

Let's denote the distance from Liz's house to Roy's house as x. According to the Pythagorean theorem, we have:

x^2 + 3^2 = 4^2

Solving this equation for x gives:

x^2 = 4^2 - 3^2
x^2 = 16 - 9
x^2 = 7

Taking the square root of both sides gives:

x = sqrt(7) ≈ 2.6

So, Liz's house is approximately 2.6 miles from Roy's house.

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