Grade 8 Algebra: Word Problems: The Pythagorean Theorem

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Multi-step problems

1. Solve:
$\text{A}$ $\text{box}$ $\text{is}$ $\text{3}$ $\text{ft}$ $\text{long,}$ $\text{4}$ $\text{ft}$ $\text{wide}$ $\text{and}$ $\text{12}$ $\text{ft}$ $\text{tall.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{the}$ $\text{diagonal}$ $\text{from}$ $\text{a}$ $\text{bottom}$ $\text{corner}$ $\text{to}$ $\text{the}$ $\text{opposite}$ $\text{top}$ $\text{corner?}$
2. Solve:
$\text{Two}$ $\text{cars}$ $\text{leave}$ $\text{the}$ $\text{same}$ $\text{spot.}$ $\text{One}$ $\text{drives}$ $\text{40}$ $\text{miles}$ $\text{north}$ $\text{and}$ $\text{the}$ $\text{other}$ $\text{drives}$ $\text{30}$ $\text{miles}$ $\text{east.}$ $\text{How}$ $\text{far}$ $\text{apart}$ $\text{are}$ $\text{they?}$
3. Solve:
$\text{A}$ $\text{TV}$ $\text{has}$ $\text{a}$ $\text{50}$ $\text{in}$ $\text{diagonal}$ $\text{and}$ $\text{is}$ $\text{40}$ $\text{in}$ $\text{wide.}$ $\text{How}$ $\text{tall}$ $\text{is}$ $\text{it?}$
4. Solve:
$\text{Is}$ $\text{a}$ $\text{triangle}$ $\text{with}$ $\text{sides}$ $\text{9}$ $\text{cm,}$ $\text{12}$ $\text{cm}$ $\text{and}$ $\text{16}$ $\text{cm}$ $\text{a}$ $\text{right}$ $\text{triangle?}$ $\text{Explain.}$
5. Solve:
$\text{A}$ $\text{13}$ $\text{ft}$ $\text{ladder}$ $\text{reaches}$ $\text{12}$ $\text{ft}$ $\text{up}$ $\text{a}$ $\text{wall.}$ $\text{Its}$ $\text{base}$ $\text{then}$ $\text{slides}$ $\text{3}$ $\text{ft}$ $\text{farther}$ $\text{out.}$ $\text{How}$ $\text{high}$ $\text{does}$ $\text{it}$ $\text{reach}$ $\text{now,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth?}$
6. Solve:
$\text{A}$ $\text{square}$ $\text{has}$ $\text{a}$ $\text{diagonal}$ $\text{of}$ $\text{10}$ $\text{cm.}$ $\text{Find}$ $\text{its}$ $\text{side}$ $\text{length}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth.}$
7. Solve:
$\text{A}$ $\text{cube}$ $\text{has}$ $\text{edges}$ $\text{of}$ $\text{2}$ $\text{meters.}$ $\text{Find}$ $\text{the}$ $\text{diagonal}$ $\text{across}$ $\text{one}$ $\text{face,}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{tenth.}$
8. Solve:
$\text{A}$ $\text{rectangle}$ $\text{has}$ $\text{a}$ $\text{diagonal}$ $\text{of}$ $\text{17}$ $\text{in}$ $\text{and}$ $\text{a}$ $\text{width}$ $\text{of}$ $\text{8}$ $\text{in.}$ $\text{Find}$ $\text{its}$ $\text{area.}$