7. Solve. Draw a diagram if needed.

a. Jack rode his bike 10 miles in 30 minutes. What was his approximate speed in mph?

b. Chris placed a ladder 4 ft from the base of a 12 ft wall. If the ladder reaches the top of the wall, how tall is the ladder?

c. A TV's size is determined by the diagonal measure of its screen. What size TV has dimensions 18 in. by 24 in.?



Answer :

Sure, let's solve these problems step-by-step:

### Part a:
Jack rode his bike 10 miles in 30 minutes.

1. Convert the time from minutes to hours:
[tex]\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \][/tex]

2. Calculate the speed in miles per hour (mph) using the formula:
[tex]\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]
Substituting the values:
[tex]\[ \text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ mph} \][/tex]

So, Jack's speed is 20 mph.

### Part b:
Chris placed a ladder 4 feet from the base of a 12-foot wall. We need to determine the length of the ladder.

Here, we can use the Pythagorean theorem because the ladder, the wall, and the ground form a right triangle. Let [tex]\( L \)[/tex] be the length of the ladder:

1. According to the Pythagorean theorem:
[tex]\[ L^2 = \text{base}^2 + \text{height}^2 \][/tex]
Substituting the values:
[tex]\[ L^2 = 4^2 + 12^2 = 16 + 144 = 160 \][/tex]

2. Solving for [tex]\( L \)[/tex] by taking the square root of both sides:
[tex]\[ L = \sqrt{160} \approx 12.65 \text{ feet} \][/tex]

So, the ladder is approximately 12.65 feet long.

### Part c:
A TV's size is determined by the diagonal measurement of its screen. We need to find the size of a TV with dimensions 18 inches by 24 inches.

Again, we can use the Pythagorean theorem. Let [tex]\( D \)[/tex] be the diagonal size of the TV:

1. According to the Pythagorean theorem:
[tex]\[ D^2 = \text{width}^2 + \text{height}^2 \][/tex]
Substituting the values:
[tex]\[ D^2 = 18^2 + 24^2 = 324 + 576 = 900 \][/tex]

2. Solving for [tex]\( D \)[/tex] by taking the square root of both sides:
[tex]\[ D = \sqrt{900} = 30 \text{ inches} \][/tex]

So, the size of the TV is 30 inches.

### Summary
- Jack's speed is 20 mph.
- The ladder is approximately 12.65 feet long.
- The TV size is 30 inches.