Question

solve. 4 trevor is building a doghouse from a scale drawing. the scale he uses is 1 in.:0.4 ft. what is the actual area of the floor of the doghouse, in square feet, if the dimensions on the scale drawing are 8 in. by 10 in.? show your work. solution: 5 juanita says that a scale of 1 in.:0.4 ft is equivalent to the ratio 6 in.:2.4 ft. do you agree? explain why or why not. 6 a car is 12.8 feet long. jane uses a scale of 1 in.:2 ft to make a model of the car. how long is her model? 7 miko drew this scale drawing of two famous landmarks. miko used a scale of 1 in.:400 ft. use equations to find the actual heights of the two structures. what is the approximate difference in their heights? show your work. solution:

Explanation:

Step1: Find actual dimensions for dog - house

The scale is 1 in. : 0.4 ft. For a length of 8 in. on the scale - drawing, the actual length $L$ is $L = 8\times0.4=3.2$ ft. For a width of 10 in. on the scale - drawing, the actual width $W$ is $W = 10\times0.4 = 4$ ft.

Step2: Calculate actual area of dog - house

The area formula is $A = L\times W$. Substituting the values of $L$ and $W$, we get $A=3.2\times4 = 12.8$ square feet.

Step3: Check scale equivalence for Juanita's statement

For the scale 1 in. : 0.4 ft, if we multiply both sides by 6, we get 6 in. : $(0.4\times6)$ ft = 6 in. : 2.4 ft. So, Juanita is correct.

Step4: Find length of car model

The scale is 1 in. : 2 ft. Let the length of the model be $x$ inches. We set up a proportion $\frac{1}{2}=\frac{x}{12.8}$. Cross - multiplying gives $2x = 12.8$, so $x=\frac{12.8}{2}=6.4$ inches.

Step5: Assume heights on scale - drawing for landmarks

Let the height of the Space Needle on the scale - drawing be $h_1$ inches and the height of the Eiffel Tower on the scale - drawing be $h_2$ inches. Let the actual heights be $H_1$ and $H_2$ respectively. Using the scale 1 in. : 400 ft, we have $H_1 = 400h_1$ and $H_2 = 400h_2$. The difference in actual heights $\Delta H=400|h_1 - h_2|$. But since the scale - drawing heights are not given, we can't calculate a numerical value for the difference.

Answer:

1. The actual area of the dog - house floor is 12.8 square feet.
2. Juanita is correct because when we multiply both parts of the ratio 1 in. : 0.4 ft by 6, we get 6 in. : 2.4 ft.
3. The length of Jane's car model is 6.4 inches.
4. We need the heights of the landmarks on the scale - drawing to find the actual heights and their difference using the scale 1 in. : 400 ft.