Back to Apply geometry to design problems — Problem 3 · Task Set 43

Exercises: Apply Geometric Methods to Solve Design Problems

Show your work for each problem. When a problem asks you to round, round to the place the
problem names. Several problems ask you to explain a design decision rather than compute a
number — for those, write in complete sentences.

Grade 10·23 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-mg-a-3

Work through problems with immediate feedback

Warm-Up: Review What You Know

These problems review formulas and ideas you have already learned.

A storage bin must fit on a shelf that is $40$ cm deep. Which inequality states this requirement, if $d$ is the depth of the bin?

$d \geq 40$ , because a bin needs to reach the back wall of the shelf in order to sit stably, so its depth has to be at least the shelf depth.

$d = 40$ , because a bin designed for a $40$ cm shelf is built to exactly that depth.

$d \leq 40$ , because the bin's depth can be anything up to the shelf depth but no more.

$40d \leq 1600$ , because the shelf's footprint sets a total area budget, and the bin's depth has to be scaled against that budget rather than against a single length.