AlgebraStructure & Method · Book 1All Chapters

Problem Solving

4-9Area Problems

Overview

Translate geometric facts into algebra: areas, perimeters, and dimensions in terms of a variable.

Key ideas

  • Rectangle area = lw; perimeter = 2l + 2w.
  • Let unknown side be a variable.
  • Use the given relationship to write an equation.

Worked examples

Example 1

Problem. A rectangle’s length is 3 more than its width; area is 40. Find dimensions.

Solution. w(w + 3) = 40 → w^2 + 3w − 40 = 0 → (w + 8)(w − 5) = 0 → w = 5; length = 8.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Rectangle: length = 2·width, area = 50. Find dimensions.

  2. 2.

    Square: area = 81. Find side.

  3. 3.

    Rectangle: perimeter = 30, width = 6. Find length.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    A rectangle has length 3 more than twice its width. If the area is 44, find the dimensions.

  2. 2.

    A triangle has base 6 and height that is 2 less than twice the base. Find the area.