BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 16P
To determine

To find: The function that models the perimeter of right triangle in terms of its shorter length whose one leg is twice as long as other leg.

Expert Solution

Answer to Problem 16P

The function that model the perimeter is P(x)=x(3+5).

Explanation of Solution

Draw the diagram of right triangle as shown in the figure below.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 16P

Let OA be x, AB be y and as per given condition OB is 2x.

Apply Pythagorean Theorem in triangle AOB

(AB)2=(OA)2+(OB)2

Substitute y for AB, x for OA and 2x for OB in above equation.

(y)2=(x)2+(2x)2y2=x2+4x2y2=5x2

Take square root of above equation.

y=5x

Perimeter of a triangle is sum of all the sides.

P=x+2x+y=3x+y

Substitute 5x for y in above equation.

P=3x+5x=x(3+5)

Thus, the function that models the perimeter of the triangle is P(x)=x(3+5).

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