WP8 - Solve Triangle using Pythagorean Theorem

In this lesson, students will learn how to solve a Pythagorean theorem word problem through step-by-step instruction. The problem requires knowledge of the theorem and the ability to solve quadratic equations. Students will learn to draw and label a right triangle and apply the theorem to determine the length of the hypotenuse, the longest side of the triangle. The lesson provides clear examples and explanations to help students grasp the concepts and apply them to similar problems.

Find the lengths of the sides of the right triangle shown on the diagram. This is a Word Problem you solve by writing an equation and factoring.

• If in a right triangle, the longest leg is 7 feet longer than the shortest leg and the hypotenuse is 1 foot longer than twice the length of the shortest leg, what is the length of the hypotenuse?
• How do you draw a picture of a triangle with dimensions from a word problem?
• If a right triangle has legs x and x + 7, and the hypotenuse is 2x + 1, what does x equal?
• How can you use the Pythagorean Theorem to solve a right triangle if each side has a variable in it?
• How do you solve (2x + 1)^2 = x^2 + (x + 7)^2?
• How do you solve 2x^2 - 10x - 48 = 0?
• How do you solve x^2 - 5x - 24 = 0?
• Why does x = -3 not work as a solution to a quadratic equation in a triangle word problem with side lengths x, x + 7, and 2x + 1?
• How do you check your solution to a triangle word problem?