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The two rectangles below have the same height-to-width ratio. Which is the value of w?

The two rectangles below have the same height-to-width ratio. Which is the value of-example-1
User Haatschii
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Final answer:

To determine 'w', the width of a rectangle with the same height-to-width ratio as a given proportion, we set up a proportion comparing the known and unknown measurements. Using cross-multiplication, we solve for 'w'. The consistent use of units throughout the calculation is essential for accuracy.

Step-by-step explanation:

To find the value of w when the rectangles have the same height-to-width ratio, we employ proportions. A proportion expresses the relationship between two ratios or fractions. In this context, we will be comparing the scale of a drawing or model to the actual dimensions of the object it represents. By setting the two height-to-width ratios equal to one another, we ultimately solve for the unknown variable w.

As an example, if the proportion is given by scale/actual equals 1/50, and we have length ratios such as 0.5 on a scale drawing to 5 feet in reality, we set up the equation 1/50 = 0.5/5 to solve for the actual length. Similarly, for width, if our scale/actual ratio is w/10 equals 0.5/5, we use cross-multiplication to solve for w. In this specific case, there is a given example of the proportion 1/48 equals w/16. By cross-multiplying (1 times 16 = 48 times w), we can find that w equals 100 feet.

It's crucial to maintain consistency in units when working with proportions. If the proportion involves feet, we keep all measurements in feet to solve for w.

User Igby Largeman
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5 votes
we know that
if the two rectangles have the same height-to-width ratio
so
height-to-width ratio larger rectangle
21/34---> equation 1
height-to-width ratio smaller rectangle
10/w----> equation 2

equate equation 1 and equation 2

21/34=10/w---------> 21*w=34*10------> w=34*10/21-----> w=16.19

the answer is
w=16.19
User Brian Gradin
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