A contractor drew up plans for an addition to a house. The new outside wallswill be a total of 80 ft in length. The contractor wants to maximize the area ofthis new addition.extension wallCurrent HouseNew Additionparallel wallextension wallComplete the statements below by filling in the blanks with the correct values.Press each hotspot and type the correct amount. Press "Submit" to save each response.The maximum possible area of the newaddition is ft².The length of the two extension walls willeach beft.The length of the parallel wall will beft.

A contractor drew up plans for an addition to a housse. The new outside walls will be a total of 80 ft in length. The contractor wants to maximize the area of this new addition. Then we have to complete the statements by filling in the blanks with the correct values.To maximize the area of the new addition, we need to consider the shape of the addition. Since you mentioned that the new outside walls will be a total of 80 ft in length, let's denote the lengths of the extension walls and parallel walls as and . Therefore, the constraint is that (Since current house wall is already present there)Now, the area of the rectangular addition is given by . We want to maximize this area A which is constraint by Therefore, the area is Setting A'(x) equal to zero, we have Now that we have the value of , substitute it back into the expression for . We have So, the dimensions that maximize the area are ft and ft. The maximum area is The maximum possible area of the new addition is 800 ft2.The length of the two extension walls will each be 20 ft.The length of the parallel wall will be 40 ft.