All courses Math III · G-MG.3 41 of 55

Use geometric methods to solve design problems under constraints such as cost, space, or ratios.

Model and maximize fixed-fencing rectangle area

Problem

A rectangle has perimeter 40 units. Let one side be x.

A dimensioned rectangle shows side lengths x and y and a fixed perimeter of 40; the area model and maximizing dimensions are withheld.

Your answer

A constraint=2x+2y=40 -> y=20-x; area model=uses x+y instead of xy; feasible domain=0<x<20; maximizing input=not area vertex; dimensions/area=incorrect B constraint=uses x+y as total fencing without side multiplicities; area model=incorrect; feasible domain=incorrect; maximizing input=incorrect; dimensions/area=incorrect C constraint=2x+2y=40 -> y=20-x; area model=A(x)=x(20-x); feasible domain=0<x<20; maximizing input=x=10; dimensions=10 by 10 units; maximum area=100 square units D constraint=2x+2y=40 -> y=20-x; area model=A(x)=x(20-x); feasible domain=includes degenerate endpoints; maximizing input=endpoint; dimensions=zero-area rectangle; maximum area=0

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Model and maximize fixed-fencing rectangle area

Explore all four courses.

Follow a skill back to its prerequisites.

Hint

Solution walkthrough

Write fencing constraint

Build model and domain

Find quadratic vertex

Recover dimensions and area

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Another way

Common mistake