A paper manufacturer is evaluating their packing procedures. Currently, they package twelve reams of paper in a box—in three stacks of four reams. However, their company has been getting complaints from the retail stores that the box is too large and heavy for the average consumer to carry by their self. So, they have decided to reduce the weight of each box by ten pounds. You have been asked to explore the different packing options based on the new weight condition and present your recommendation to the CEO of the paper company. Calculate the volume of each box you described in the three ways to package the reams of paper. Are you surprised by the results? Why or why not?

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality