Question

The floor of a rectangular living room is 12 feet by 16 feet. What is the distance between

opposite corners of the living room?

Answer 1

The width of Dana's living room is 16 feet.

Step-by-step explanation:

Because Dana's living room is rectangular and we are given the length of one side and the length of the diagonal we can use the Pythagorean Theorem to solve this problem.

For a right triangle which the length, width and diagonal make up the Pythagorean Theorem states:

a

2

+

b

2

=

c

2

Let the length of 12 be

a

and because the diagonal is the hypotenuse of the triangle (the side opposite the right angle) we let

c

be 20. Substituting and solving gives:

12

2

+

b

2

=

20

2

144

+

b

2

=

400

144

−

144

+

b

2

=

400

−

144

0

+

b

2

=

256

b

2

=

256

√

b

2

=

√

256

b

=

16

Answer 2

The distance between opposite corners of a rectangular living room that measures 12 feet by 16 feet is approximately 20 feet.

Explanation:

To find the distance between opposite corners of a rectangle, 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 other two sides. In this case, the length and width of the living room will be the two sides of the triangle and the distance between opposite corners will be the hypotenuse.

We can label the length as a and the width as b. Therefore, using the Pythagorean theorem, we can write the equation a^2 + b^2 = c^2, where c is the distance between opposite corners. Plugging in the values, we get 12^2 + 16^2 = c^2. Simplifying, we get 144 + 256 = c^2. Combining like terms, we get 400 = c^2.

To find the value of c, we need to take the square root of both sides of the equation. This gives us c = √400. Taking the square root of 400, we get 20. Therefore, the distance between opposite corners of the living room is 20 feet.

In simple terms, the distance between opposite corners of a rectangular living room is equal to the square root of the sum of the squares of its length and width. This is because the diagonal of a rectangle forms a right triangle with the length and width as its sides. By using the Pythagorean theorem, we can find the length of the diagonal, which is the distance between opposite corners.

In this case, the living room measures 12 feet by 16 feet. This means that the length of one side, a, is 12 feet and the length of the other side, b, is 16 feet. By substituting these values in the Pythagorean theorem, we can find the value of c, which is the distance between opposite corners.

Hence, the distance between opposite corners of a rectangular living room that measures 12 feet by 16 feet is approximately 20 feet. This calculation can also be used to find the distance between opposite corners of any rectangle, as long as the length and width are known. By following this method, we can accurately determine the distance between opposite corners of any rectangular space.