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:
$\text{A}$ $\text{boat}$ $\text{sails}$ $\text{15}$ $\text{km}$ $\text{south}$ $\text{and}$ $\text{then}$ $\text{8}$ $\text{km}$ $\text{west.}$ $\text{How}$ $\text{far}$ $\text{is}$ $\text{it}$ $\text{from}$ $\text{the}$ $\text{dock?}$