Multiple Choice
A ladder is leaning against a wall. The foot of the ladder is meters away from the wall, and the ladder reaches a height of meters on the wall. What is the length of the ladder?
0. Review of College Algebra
Pythagorean Theorem & Basics of Triangles
Multiple Choice
Given that , , and form a Pythagorean triple, what is the value of ?
A
B
C
D
Verified step by step guidance1
Recall that a Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) such that \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (the longest side).
Identify the two given sides: 20 and 21. We need to determine if \(x\) is the hypotenuse or one of the legs. Since 21 is larger than 20, if \(x\) is larger than both, it will be the hypotenuse; otherwise, it will be a leg.
Assuming \(x\) is the hypotenuse, set up the Pythagorean equation: \(20^2 + 21^2 = x^2\).
Calculate the squares of the known sides: \(20^2 = 400\) and \(21^2 = 441\), then add them: \(400 + 441 = 841\).
Take the square root of 841 to find \(x\): \(x = \sqrt{841}\). This will give the value of \(x\) that completes the Pythagorean triple.
Related Videos
Related Practice
