34.8k views
2 votes
Hello!

I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.

If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.

Anyways, please show all of your work and explain your thinking! Thanks!

Hello! I am here with a handful of geometry questions today. Please answer the question-example-1
User BWStearns
by
3.9k points

1 Answer

4 votes

9514 1404 393

Answer:

square with side length √17 units, so area 17 square units.

Explanation:

Each side has a slope with a rise of 1 and a run of 4, or a rise of -4 and a run of 1. The ratios of these numbers are opposite reciprocals, so we know the sides are perpendicular. The sum of squares of these numbers is 17, so we know the sides are √17 and all are the same length. (The Pythagorean theorem tells us this.)

A quadrilateral with equal-length perpendicular sides is a square. This square has side length √17 units and area (√17)² = 17 square units.

User Withtaker
by
4.2k points