Question

unit: pythagorean theorem
homework 3
name
date
pd
applying the pythagorean theorem
use the pythagorean theorem to help you answer the following questions. show all work and round to the nearest tenth when necessary.

1. layne rode his bike from point a to b by using cherry street. how much further would his trip have been if he took orange drive and peach avenue instead?
2. ashton left his house and ran 4 miles east and then 3 miles north. he then took the diagonal path back home. if he burned 105 calories every mile that he ran, how many total calories did he burn on his run?
3. the blackburn family has a square field where they keep their cattle. the area of the field is 40,000 ft², and mr. blackburn wants to put a fence diagonally through the field. what should the length of the fence be?
4. martin needs to place caution tape across both diagonals of a broken rectangular door in his store. if the dimensions of the door are 3 feet by 7 feet, how many feet of caution tape will he need?
5. tony is building a doghouse, and the front view of the roof is an isosceles triangle as shown below. what is the height of the roof?
6. if the area of square 2 is 225 units², and the perimeter of square 1 is 100 units, what is the area of square 3?

©maneuvering the middle llc, 201

Explanation:

Problem 1

Step1: Find Orange Dr. length

Let Orange Dr. = $x$. Use Pythagorean theorem:
$$x = \sqrt{85^2 - 77^2} = \sqrt{7225 - 5929} = \sqrt{1296} = 36 \text{ yd}$$

Step2: Calculate total alternate distance

$$36 + 77 = 113 \text{ yd}$$

Step3: Find distance difference

$$113 - 85 = 28 \text{ yd}$$

Problem 2

Step1: Calculate diagonal run length

Let diagonal = $d$. Use Pythagorean theorem:
$$d = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ miles}$$

Step2: Find total miles run

$$4 + 3 + 5 = 12 \text{ miles}$$

Step3: Compute total calories burned

$$12 \times 105 = 1260$$

Problem 3

Step1: Find square side length

Let side = $s$. $s = \sqrt{40000} = 200 \text{ ft}$

Step2: Calculate diagonal fence length

$$\text{Diagonal} = s\sqrt{2} = 200\sqrt{2} \approx 282.8 \text{ ft}$$

Problem 4

Step1: Find one diagonal length

Let diagonal = $d$. Use Pythagorean theorem:
$$d = \sqrt{3^2 + 7^2} = \sqrt{9 + 49} = \sqrt{58} \approx 7.62 \text{ ft}$$

Step2: Total tape for two diagonals

$$2 \times 7.62 = 15.2 \text{ ft}$$

Problem 5

Step1: Split base into half

$$\frac{40}{2} = 20 \text{ inches}$$

Step2: Calculate roof height $x$

$$x = \sqrt{29^2 - 20^2} = \sqrt{841 - 400} = \sqrt{441} = 21 \text{ inches}$$

Problem 6

Step1: Find side of square 1

Side of square 1: $\frac{100}{4} = 25$ units

Step2: Find side of square 2

Side of square 2: $\sqrt{225} = 15$ units

Step3: Find side of square 3

Let side of square 3 = $a$. Use Pythagorean theorem:
$$a = \sqrt{25^2 - 15^2} = \sqrt{625 - 225} = \sqrt{400} = 20 \text{ units}$$

Step4: Calculate area of square 3

$$20^2 = 400 \text{ units}^2$$

Answer:

1. 28 yards
2. 1260 calories
3. $\approx 282.8$ feet
4. $\approx 15.2$ feet
5. 21 inches
6. 400 units$^2$