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# Squares and Square Roots

# Word Problems Exercises

### Example 1

A square has area *x*. How long is a diagonal of the square?

### Example 2

Gina needs to use a ladder to retrieve a frisbee from the roof of her house. The frisbee is 12 feet above the ground, and because of the bushes near her house the base of the ladder will need to be 5 feet from the edge of the house. How long of a ladder does Gina need?

### Example 3

Leonardo walked north for 5 miles, south for 10 miles, and then east for 8 miles. How far away from his starting point did he finish walking?

### Example 4

A right triangle has a hypotenuse of 16 inches. The legs of the right triangle are the same length as each other. How long are the legs?

### Example 5

A square has area 2*x* + 4 and side length 10. Find *x*.

### Example 6

Find the radius of the circle shown below. The hypotenuse of the triangle has length 9.

### Example 7

Dorothy wants to build a triangular garden next to her house to go with her circular pool and trapezoidal deck. Her octagonal patio furniture is still on back order. The farthest the garden will extend from her house is 40 feet. One edge of the garden will be along the side of her house, which is *L* feet long. If Dorothy puts fencing along the other two edges of the garden, the ones that aren't the side of her house, how many feet of fencing will she need? Your answer may have *L* in it.

### Example 8

A boat left port and sailed due west for 2 hours at 10 mph, then sailed north for 3 hours. It didn't want to sail in a straight line to its destination, because it was trying to avoid another boat it dated a few months back. Awkward. The boat ended up 25 miles away from port as the crow flies (along a straight line). While the boat was sailing north, how fast was it sailing?

### Example 9

To drive from her house to her office, Fran drove north at 60 mph for 10 minutes, then turned and drove east at 48 mph. She didn't want to drive in a straight line to her destination, because, um, that's not how roads work. Her office is 26 miles from her house as the crow flies. Once again, that crow is flying in a straight line. How long did it take Fran to drive from her house to her office?

### Example 10

Johnny and his older, taller brother are standing 3 feet apart from each other. Johnny has already explained that this is how much room he needs for his "personal space bubble," and his brother can respect that. Johnny was trying to balance a perfectly straight, 4-foot stick on its end on top of his head, but he lost control of it and it fell, the opposite end of it landing on top of his brother's head. If his brother is 6 feet tall, how tall is Johnny?