ALGEBRA 292
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11 – 4 Problem Solving Using the Pythagorean Theorem
Make a sketch for each problem. If an answer is not a perfect square, round to the
nearest hundredth.
1. Find the length of a diagonal of a rectangle whose dimensions are 33 inches by 56 inches.
2. The diagonal of a rectangle is 170 feet and its width is 80 feet. Find the length of the
rectangle.
3. A TV screen is measured along the diagonal of the screen. A 44 inch TV has a diagonal that
measures 44 inches. If the height of the screen is 25 inches, find the width of the screen.
4. A baseball diamond is a square, with each side 90 feet.
a) What is the length from first base to third base?
b) Is this the same length as the distance from home plate to second base? Explain why or why
not?
Make a sketch for each problem. If an answer is not a perfect square, round to the
nearest hundredth.
5. The Reflecting Pool in front of the Lincoln Memorial in Washington, D.C., is rectangular with
a length of 2,029 feet and a width of 167 feet. To the nearest foot, what is the length of the
diagonal of the Reflecting Pool?
6. The base of an isosceles triangle is 18 inches long. The equal sides are each 24 inches
long. Find the altitude (or height) of the isosceles triangle.
7. A ladder that is 25 feet long is placed against a house. The bottom of the ladder is 10 feet
from the base of the house. How far up the house does the ladder reach?
8. The bottom of a 7 foot ramp is 5 feet from the base of a loading platform. Find the height of
the platform.