Two architects are designing a house, but they are arguing about how big the large, rectangular living room should be.
Architect 1
The first architect thinks the room should be exactly 1.75 times as long as it is wide. She thinks this will make the shape of the room most convenient for furniture and most comfortable to be in. She creates a formula where you input how wide the room will be, and it spits out an answer saying how long the room will have to be.
\ell=f_{1}(w)=1.75w
Architect 2
The second architect disagrees. He thinks Architect 1’s method makes for difficult rooms to build, since you could have a room that’s got strange fractions of a foot. He uses a different formula where he multiplies the width by 1.5 and then just adds 5 more feet.
\ell=f_{2}(w)=1.5w+5
__________________________________________________________
Obviously, the two architects disagree about how the length and width of the room should be related to each other. But, can you design a room that makes both architects happy? Explain why or why not. If a compromise is possible, what should the dimensions be?
Two architects are designing a house, but they are arguing about how big the large, rectangular living room should be.
Architect 1
The first architect thinks the room should be exactly 1.75 times as long as it is wide. She thinks this will make the shape of the room most convenient for furniture and most comfortable to be in. She creates a formula where you input how wide the room will be, and it spits out an answer saying how long the room will have to be.
Architect 2
The second architect disagrees. He thinks Architect 1’s method makes for difficult rooms to build, since you could have a room that’s got strange fractions of a foot. He uses a different formula where he multiplies the width by 1.5 and then just adds 5 more feet.
__________________________________________________________
Obviously, the two architects disagree about how the length and width of the room should be related to each other. But, can you design a room that makes both architects happy? Explain why or why not. If a compromise is possible, what should the dimensions be?