Grade 8 Algebra: Word Problems: The Pythagorean Theorem

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Whole-number answers

1. Solve:
$\text{A}$ $\text{10}$ $\text{ft}$ $\text{ladder}$ $\text{leans}$ $\text{against}$ $\text{a}$ $\text{wall}$ $\text{with}$ $\text{its}$ $\text{base}$ $\text{6}$ $\text{ft}$ $\text{from}$ $\text{the}$ $\text{wall.}$ $\text{How}$ $\text{high}$ $\text{up}$ $\text{the}$ $\text{wall}$ $\text{does}$ $\text{it}$ $\text{reach?}$
2. Solve:
$\text{A}$ $\text{TV}$ $\text{screen}$ $\text{is}$ $\text{16}$ $\text{in}$ $\text{wide}$ $\text{and}$ $\text{12}$ $\text{in}$ $\text{tall.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{its}$ $\text{diagonal?}$
3. Solve:
$\text{Lea}$ $\text{walks}$ $\text{9}$ $\text{blocks}$ $\text{east}$ $\text{and}$ $\text{then}$ $\text{12}$ $\text{blocks}$ $\text{north.}$ $\text{How}$ $\text{far}$ $\text{is}$ $\text{she}$ $\text{from}$ $\text{her}$ $\text{start}$ $\text{in}$ $\text{a}$ $\text{straight}$ $\text{line?}$
4. Solve:
$\text{A}$ $\text{rectangular}$ $\text{park}$ $\text{is}$ $\text{5}$ $\text{meters}$ $\text{by}$ $\text{12}$ $\text{meters.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{the}$ $\text{diagonal}$ $\text{path}$ $\text{across}$ $\text{it?}$
5. Solve:
$\text{A}$ $\text{kite}$ $\text{string}$ $\text{is}$ $\text{25}$ $\text{meters}$ $\text{long.}$ $\text{The}$ $\text{kite}$ $\text{is}$ $\text{directly}$ $\text{above}$ $\text{a}$ $\text{spot}$ $\text{7}$ $\text{meters}$ $\text{from}$ $\text{you.}$ $\text{How}$ $\text{high}$ $\text{is}$ $\text{the}$ $\text{kite?}$
6. Solve:
$\text{A}$ $\text{ramp}$ $\text{rises}$ $\text{3}$ $\text{ft}$ $\text{over}$ $\text{a}$ $\text{ground}$ $\text{distance}$ $\text{of}$ $\text{4}$ $\text{ft.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{the}$ $\text{ramp?}$
7. Solve:
$\text{A}$ $\text{tent}$ $\text{pole}$ $\text{is}$ $\text{8}$ $\text{ft}$ $\text{tall.}$ $\text{A}$ $\text{rope}$ $\text{runs}$ $\text{from}$ $\text{its}$ $\text{top}$ $\text{to}$ $\text{a}$ $\text{stake}$ $\text{6}$ $\text{ft}$ $\text{from}$ $\text{its}$ $\text{base.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{the}$ $\text{rope?}$
8. Solve:
$\text{A}$ $\text{boat}$ $\text{sails}$ $\text{15}$ $\text{km}$ $\text{south}$ $\text{and}$ $\text{then}$ $\text{8}$ $\text{km}$ $\text{west.}$ $\text{How}$ $\text{far}$ $\text{is}$ $\text{it}$ $\text{from}$ $\text{the}$ $\text{dock?}$

Answer Key

Level 1

1. $8\text{ ft}$
2. $20\text{ in}$
3. $15\text{ blocks}$
4. $13\text{ meters}$
5. $24\text{ meters}$
6. $5\text{ ft}$
7. $10\text{ ft}$
8. $17\text{ km}$

Grade 8 Algebra: Word Problems: The Pythagorean Theorem

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Rounding to the nearest tenth

1. Solve:
$\text{A}$ $\text{square}$ $\text{field}$ $\text{has}$ $\text{sides}$ $\text{of}$ $\text{50}$ $\text{meters.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{its}$ $\text{diagonal,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$
2. Solve:
$\text{A}$ $\text{12}$ $\text{ft}$ $\text{ladder}$ $\text{has}$ $\text{its}$ $\text{base}$ $\text{4}$ $\text{ft}$ $\text{from}$ $\text{a}$ $\text{wall.}$ $\text{How}$ $\text{high}$ $\text{does}$ $\text{it}$ $\text{reach,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$
3. Solve:
$\text{A}$ $\text{phone}$ $\text{screen}$ $\text{is}$ $\text{6}$ $\text{cm}$ $\text{wide}$ $\text{and}$ $\text{13}$ $\text{cm}$ $\text{tall.}$ $\text{Find}$ $\text{its}$ $\text{diagonal}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth.}$
4. Solve:
$\text{A}$ $\text{soccer}$ $\text{field}$ $\text{is}$ $\text{100}$ $\text{meters}$ $\text{long}$ $\text{and}$ $\text{60}$ $\text{meters}$ $\text{wide.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{its}$ $\text{diagonal,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$
5. Solve:
$\text{A}$ $\text{plane}$ $\text{flies}$ $\text{30}$ $\text{km}$ $\text{north}$ $\text{and}$ $\text{then}$ $\text{40}$ $\text{km}$ $\text{east.}$ $\text{How}$ $\text{far}$ $\text{is}$ $\text{it}$ $\text{from}$ $\text{where}$ $\text{it}$ $\text{started?}$
6. Solve:
$\text{A}$ $\text{20}$ $\text{ft}$ $\text{wire}$ $\text{runs}$ $\text{from}$ $\text{the}$ $\text{top}$ $\text{of}$ $\text{a}$ $\text{pole}$ $\text{to}$ $\text{a}$ $\text{stake}$ $\text{9}$ $\text{ft}$ $\text{from}$ $\text{its}$ $\text{base.}$ $\text{How}$ $\text{tall}$ $\text{is}$ $\text{the}$ $\text{pole,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$
7. Solve:
$\text{A}$ $\text{bike}$ $\text{trail}$ $\text{goes}$ $\text{3}$ $\text{miles}$ $\text{west}$ $\text{and}$ $\text{then}$ $\text{7}$ $\text{miles}$ $\text{south.}$ $\text{How}$ $\text{far}$ $\text{is}$ $\text{the}$ $\text{straight}$ $\text{path}$ $\text{back,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$
8. Solve:
$\text{A}$ $\text{box}$ $\text{is}$ $\text{10}$ $\text{in}$ $\text{long}$ $\text{and}$ $\text{7}$ $\text{in}$ $\text{wide.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{longest}$ $\text{pencil}$ $\text{that}$ $\text{can}$ $\text{lie}$ $\text{flat}$ $\text{on}$ $\text{its}$ $\text{bottom,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$

Answer Key

Level 2

1. $50\sqrt{2} \approx 70.7\text{ meters}$
2. $\sqrt{128} \approx 11.3\text{ ft}$
3. $\sqrt{205} \approx 14.3\text{ cm}$
4. $\sqrt{13600} \approx 116.6\text{ meters}$
5. $50\text{ km}$
6. $\sqrt{319} \approx 17.9\text{ ft}$
7. $\sqrt{58} \approx 7.6\text{ miles}$
8. $\sqrt{149} \approx 12.2\text{ in}$

Answer Key

Level 3

1. $13\text{ ft}$
2. $50\text{ miles}$
3. $30\text{ in}$
4. $\text{No: } 81+144=225 \ne 256$
5. $\sqrt{105} \approx 10.2\text{ ft}$
6. $5\sqrt{2} \approx 7.1\text{ cm}$
7. $2\sqrt{2} \approx 2.8\text{ meters}$
8. $120\text{ square inches}$