Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Answer:
17 cm
Step-by-step explanation:
You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.
Pythagorean theorem
The relation between the side lengths in the right triangle is ...
a² +b² = c²
Application
Substituting the given relations, we have ...
a² +(2a-1)² = (2a+1)²
a² +4a² -4a +1 = 4a² +4a +1
a² -8a = 0 . . . . . . write in standard form
a(a -8) = 0 . . . . . . factor
a = 0 or a = 8
We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...
c = 2(8) +1 = 17
The hypotenuse is 17 cm.
__
Additional comment
You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.