Answered: You are given that the two…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 22E

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Question

You are given that the two nonhypotenuse sides of a right triangle add up to 10 inches. What is the maximum area of the triangle? Can you generalize
this result?

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Expert Solution

Step 1

Given: The two non-hypotenuse sides of a right triangle add up to 10 inches.

Step 2

To find: The maximum area of a triangle.

We have given that the two non-hypotenuse sides of a right triangle add up to 10 inches.

Let the two non-hypotenuse sides be $x$ and $y$ .

So $x + y = 10$ .

$\Rightarrow y = 10 - x$ .

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