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

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

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