Question

What is the ratio between the area of the bedroom and the area of the den?

Answer 1

The bedroom floor and den floor is similar. So ratio of areas of bedroom floor and den floor is equal to square of ratio of corresponding sides.

Determine the ratio of area of bedroom floor and den floor.

`\begin{gathered} \frac{Bedroom_{}}{\text{Den}}=((14)/(20))^2 \\ =((7)/(10))^2 \\ =(49)/(100) \end{gathered}`

So ratio of area of bedroom to area of Den is 49:100.

The cost of carpet depends upon the area of the floor as same carpet is used nd sold by rate of per square foot. So ratio of cost to carpet the bedroom to cost to carpet the den is 49:100.

Determine the cost to carpet the den.

`\begin{gathered} \text{ }\frac{C_(bedroom)}{C_{\text{Den}}}=(49)/(100) \\ (120)/(C_(Den))=(49)/(100) \\ C_(Den)=120\cdot(100)/(49) \\ =244.8979 \\ \approx244.90 \end{gathered}`

So cost to carpet the den is $244.90.