Question

solve the problems below. estimate your final answer to the nearest tenth if necessary. make sure to show all your work

1. calculate the length of the diagonal of a square with sides of length 6 cm.
2. john leaves school to go home. he walks 6 blocks north and then 8 blocks west. how far is john from the school?
3. the bottom of a ladder must be placed 3 feet from a wall. the ladder is 12 feet long. how far above the ground does the ladder touch the wall?
4. donna’s tv screen is 20 inches long. if the diagonal measures 25 inches, how long is the width of donna’s tv?

Explanation:

Problem 3

Step1: Apply Pythagorean theorem

For a square with side $s$, diagonal $d = \sqrt{s^2 + s^2}$

Step2: Substitute $s=6$ cm

$d = \sqrt{6^2 + 6^2} = \sqrt{36+36} = \sqrt{72}$

Step3: Simplify and round

$\sqrt{72} \approx 8.5$ cm

Problem 4

Step1: Apply Pythagorean theorem

Distance $d = \sqrt{6^2 + 8^2}$

Step2: Calculate squares and sum

$d = \sqrt{36+64} = \sqrt{100}$

Step3: Simplify

$\sqrt{100} = 10$ blocks

Problem 5

Step1: Apply Pythagorean theorem

Height $h = \sqrt{12^2 - 3^2}$

Step2: Calculate squares and difference

$h = \sqrt{144-9} = \sqrt{135}$

Step3: Simplify and round

$\sqrt{135} \approx 11.6$ feet

Problem 6

Step1: Apply Pythagorean theorem

Width $w = \sqrt{25^2 - 20^2}$

Step2: Calculate squares and difference

$w = \sqrt{625-400} = \sqrt{225}$

Step3: Simplify

$\sqrt{225} = 15$ inches

Answer:

1. 8.5 cm
2. 10 blocks
3. 11.6 feet
4. 15 inches