Question

5. The diagonal of a rectangle is 25 in. The width is 15 inches. What is the length?

6. Two sides of a right triangle are 8 and 12. Find the hypotenuse.

7. A baseball diamond is a square that is 90 feet on each side. What is the distance a
catcher has to throw the ball from home to second base?

8. David leaves the house to go to school. He walks 200m west and 125m north. How far
away is he from his starting point? (the diagonal)

9. A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is
your walk if you walk diagonally across the park than along the two sides of it?

Answer 1

5. Using the Pythagorean theorem, we can find the length of the rectangle.

a^2 + b^2 = c^2

15^2 + b^2 = 25^2

225 + b^2 = 625

b^2 = 400

b = 20

So the length of the rectangle is 20 inches.

6. Using the Pythagorean theorem, we can find the hypotenuse of the right triangle.

a^2 + b^2 = c^2

8^2 + 12^2 = c^2

64 + 144 = c^2

208 = c^2

c = sqrt(208) = 14.4222

So the hypotenuse of the right triangle is approximately 14.4222.

7. The distance from home to second base is the diagonal of the square, which we can find using the Pythagorean theorem.

a^2 + b^2 = c^2

90^2 + 90^2 = c^2

8100 + 8100 = c^2

16200 = c^2

c = sqrt(16200) = 127.2792

So the distance a catcher has to throw the ball from home to second base is approximately 127.2792 feet.

8. We can use the Pythagorean theorem to find the distance from David's starting point to his current location.

a^2 + b^2 = c^2

200^2 + 125^2 = c^2

40000 + 15625 = c^2

55625 = c^2

c = sqrt(55625) = 235.7023

So David is approximately 235.7023 meters away from his starting point.

9. We can use the Pythagorean theorem to find the length of the diagonal of the park.

a^2 + b^2 = c^2

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c = sqrt(100) = 10

So the length of the diagonal of the park is 10 miles.

If we walk along the two sides of the park, we would walk a total of 8 + 6 + 8 + 6 = 28 miles.

If we walk diagonally across the park, we would walk a distance of

Answer 2

Answer: i have it below

Explanation:

5. The length is 20 inches

6. The hypotenuse is 12 inches

7. Distance is 127.3 feet

8. He is 235.8 meters away from where he started

9. It will be 4 miles shorter if you walk diagonally across the park