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Q1: A picture is 10 in wide and 8 in tall. To display on a web page, the picture must be reduced to 3.5 in tall. How wide
should the picture be on the web for the pictures to be similar?

 

Q2:A picture is 10 inches tall, 14 inches wide and scaled down to 2 inches tall. How wide is the picture?

 

Q3:A t-shirt design includes an isosceles triangle with sides 4.5 in, 4.5, and base of 6 in. The enlarged version is 3 feet
long on each of the two sides. What is the third side (base) length?

 

Q4:The distance between two cities, A and B, is 120 miles. What is the distance between the cities on a
map, if 1 mile is represented by 0.03 inches on the map?

 

Thats the last pls answer these in order.

AndyTefer05  Sep 28, 2017

Best Answer 

 #2
avatar+4753 
+2

1)   We want the ratio of width to height to be the same. If we multiply the height by 2, we must

      multiply the width by 2. If we multiply the height by  x , we must multiply the width by  x .

      The number that we multiply the height and width by is the scale factor.

 

\(\frac{\text{old width}}{\text{old height}}\,=\,\frac{\text{new width}}{\text{new height}} \\~\\ \frac{10}{8}\,=\,\frac{\text{new width}}{3.5} \\~\\ 3.5\,*\,\frac{10}{8}\,=\,\text{new width} \\~\\ 4.375\,=\,\text{new width, in inches}\)          Plug in the information from the problem.

 

--------------------

 

2)   This is done the same as the last question.

 

\(\frac{\text{old width}}{\text{old height}}=\frac{\text{new width}}{\text{new height}} \)          Plug in the information from the problem.

 

\(\frac{14}{10}=\frac{\text{new width}}{2}\)          Can you finish it from here?  smiley

 

--------------------

 

3)   First let's convert 3 feet into inches.   1 ft  =  12 in   →   3 ft  =  36 in

 

Now let's call the unknown scale factor  " s " .

 

4.5s  =  36      Divide both sides by  4.5 .

     s  =  8

 

So each side of the triangle is multiplied by  8  .

The base of the larger triangle will then   =   (8 * 6) inches   =   48 inches   =   4 feet

 

--------------------

 

4)   If it takes 0.03 inches to make 1 mile on the map, then it will take 0.03 * 120 inches to make 120

      miles on the map...which is 3.6 inches.

hectictar  Sep 29, 2017
Sort: 

1+0 Answers

 #2
avatar+4753 
+2
Best Answer

1)   We want the ratio of width to height to be the same. If we multiply the height by 2, we must

      multiply the width by 2. If we multiply the height by  x , we must multiply the width by  x .

      The number that we multiply the height and width by is the scale factor.

 

\(\frac{\text{old width}}{\text{old height}}\,=\,\frac{\text{new width}}{\text{new height}} \\~\\ \frac{10}{8}\,=\,\frac{\text{new width}}{3.5} \\~\\ 3.5\,*\,\frac{10}{8}\,=\,\text{new width} \\~\\ 4.375\,=\,\text{new width, in inches}\)          Plug in the information from the problem.

 

--------------------

 

2)   This is done the same as the last question.

 

\(\frac{\text{old width}}{\text{old height}}=\frac{\text{new width}}{\text{new height}} \)          Plug in the information from the problem.

 

\(\frac{14}{10}=\frac{\text{new width}}{2}\)          Can you finish it from here?  smiley

 

--------------------

 

3)   First let's convert 3 feet into inches.   1 ft  =  12 in   →   3 ft  =  36 in

 

Now let's call the unknown scale factor  " s " .

 

4.5s  =  36      Divide both sides by  4.5 .

     s  =  8

 

So each side of the triangle is multiplied by  8  .

The base of the larger triangle will then   =   (8 * 6) inches   =   48 inches   =   4 feet

 

--------------------

 

4)   If it takes 0.03 inches to make 1 mile on the map, then it will take 0.03 * 120 inches to make 120

      miles on the map...which is 3.6 inches.

hectictar  Sep 29, 2017

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