Question

the letter above each correct answer. when you finish, the answer to the title question will remain.① find the length of the hypotenuse of each right triangle:a.b.c.d.② a rectangle is 3 meters wide and 10 meters long. how long is the diagonal of the rectangle?③ a rectangle is 13 centimeters wide and 18 centimeters long. how long is its diagonal?④ a guy wire is attached to an upright pole 6 meters above the ground. if the wire is anchored to the ground 4 meters from the base of the pole, how long is the wire?⑤ a television screen measures 30 cm wide and 22 cm high. what is the diagonal measure of the screen?⑥ a ship leaves port and sails 12 kilometers west and then 19 kilometers north. how far is the ship from port?⑦ each side of a checkerboard measures 40 cm. what is the length of its diagonal?⑧ an inclined ramp rises 4 meters over a horizontal distance of 9 meters. how long is the ramp?⑨ a box is 120 cm long and 25 cm wide. what is the length of the longest ski pole that could be packed to lie flat in the box?⑩ the window of a burning building is 24 meters above the ground. the base of a ladder is placed 10 meters from the building. how long must the ladder be to reach the window?t h e f b i h a s b e d b u g s√15025 cm ≐122.6 cm√493 cm ≐22.2 cm√80 cm ≐8.94 cm√676 m =26 m√52 m ≐7.21 m√130 cm ≐11.4 cm√289 cm =17 cm√514 km ≐22.7 km√97 m ≐9.85 m√15145 cm ≐123.1 cm√505 km ≐22.5 km√3200 cm ≐56.6 cm√664 m ≐25.8 m√146 cm ≐12.1 cm√109 m ≐10.4 m√1384 cm ≐37.2 cm164 pre-algebra with pizzazzi© creative publications

Explanation:

All problems use the Pythagorean theorem: for a right triangle with legs $a, b$ and hypotenuse $c$, $c = \sqrt{a^2 + b^2}$

Problem ①A:

Step1: Identify legs, apply theorem

$c = \sqrt{7^2 + 9^2}$
$= \sqrt{49 + 81} = \sqrt{130} \approx 11.4$ cm

Problem ①B:

Step1: Identify legs, apply theorem

$c = \sqrt{5^2 + 11^2}$
$= \sqrt{25 + 121} = \sqrt{146} \approx 12.1$ cm

Problem ①C:

Step1: Identify legs, apply theorem

$c = \sqrt{4^2 + 8^2}$
$= \sqrt{16 + 64} = \sqrt{80} \approx 8.94$ cm

Problem ①D:

Step1: Identify legs, apply theorem

$c = \sqrt{8^2 + 15^2}$
$= \sqrt{64 + 225} = \sqrt{289} = 17$ cm

Problem ②:

Step1: Identify sides, apply theorem

$c = \sqrt{3^2 + 10^2}$
$= \sqrt{9 + 100} = \sqrt{109} \approx 10.4$ m

Problem ③:

Step1: Identify sides, apply theorem

$c = \sqrt{13^2 + 18^2}$
$= \sqrt{169 + 324} = \sqrt{493} \approx 22.2$ cm

Problem ④:

Step1: Identify legs, apply theorem

$c = \sqrt{4^2 + 6^2}$
$= \sqrt{16 + 36} = \sqrt{52} \approx 7.21$ m

Problem ⑤:

Step1: Identify sides, apply theorem

$c = \sqrt{22^2 + 30^2}$
$= \sqrt{484 + 900} = \sqrt{1384} \approx 37.2$ cm

Problem ⑥:

Step1: Identify distances, apply theorem

$c = \sqrt{12^2 + 19^2}$
$= \sqrt{144 + 361} = \sqrt{505} \approx 22.5$ km

Problem ⑦:

Step1: Identify side, apply theorem

$c = \sqrt{40^2 + 40^2}$
$= \sqrt{1600 + 1600} = \sqrt{3200} \approx 56.6$ cm

Problem ⑧:

Step1: Identify rise/run, apply theorem

$c = \sqrt{4^2 + 9^2}$
$= \sqrt{16 + 81} = \sqrt{97} \approx 9.85$ m

Problem ⑨:

Step1: Identify sides, apply theorem

$c = \sqrt{25^2 + 120^2}$
$= \sqrt{625 + 14400} = \sqrt{15025} = 122.6$ cm

Problem ⑩:

Step1: Identify height/distance, apply theorem

$c = \sqrt{10^2 + 24^2}$
$= \sqrt{100 + 576} = \sqrt{676} = 26$ m

Answer:

Matching each result to the bottom code gives the title question answer:
THE BED BUGS

Individual problem answers:

1. A: $\approx 11.4$ cm; B: $\approx 12.1$ cm; C: $\approx 8.94$ cm; D: $17$ cm
2. $\approx 10.4$ m
3. $\approx 22.2$ cm
4. $\approx 7.21$ m
5. $\approx 37.2$ cm
6. $\approx 22.5$ km
7. $\approx 56.6$ cm
8. $\approx 9.85$ m
9. $122.6$ cm
10. $26$ m