Activity 23 Applying the Pythagorean Theorem

Find x in the following figure.

Find x in the following figure. Round to the nearest tenth if necessary.

Find x in the following figure. Round to the nearest tenth if necessary.

Riyo wants to place a string of lights across the ceiling of her bedroom. The room is a rectangle that is 18 feet long and 15 feet wide. Her string of lights is 20 feet long. Will the string of lights be long enough to hang diagonally from one corner of the ceiling to the other? Explain.

• No; the diagonal of the room is about 23.4 feet long.

• Yes; the diagonal of the room is about 19.8 feet long.

• None of the above.

Which of the following lengths is the greatest?

• the diagonal of a square with 4-in. sides

• the hypotenuse of a right triangle with legs of length 3 in. and 4 in.

• the diagonal of a rectangle with sides of length 5 in. and 12 in.

• the perimeter of a square with side lengths of 1 in.

The box has dimensions 25 cm, 36 cm, and x cm. The diagonal shown has a length of 65 cm. Find the value of x. Round to the nearest tenth, if necessary.

A television set’s screen size is measured along the diagonal of the screen from one corner to another. If a television screen has a length of 28 inches and a diagonal that measures 32 inches, what is the height of the screen to the nearest tenth?

Find the distance between the pair of points. Round to the nearest tenth, if necessary. (−1, 1) and (3, −2)

Find the distance between the pair of points. Round to the nearest tenth, if necessary. (−3, −5) and (5, 5)

Which is the best estimate of the distance between the points A(4, −5) and B(−2, 1)?

• 7 units

• 7.5 units

• 8 units

• 8.5 units