Question
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Scale Drawings Practice
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Question
Use the image to answer the question.
An illustration shows two similar quadrilaterals F G H J and Z Y X W. In the quadrilateral F G H J, side F J measures 5, side F G measures 6, and side H J measures 4. Side G H is unmeasured. In the quadrilateral Z Y X W, side Z W measures 10, side Z Y measures 12, and side Y X measures 14. Side XW is unmeasured. Angle F J H and angle Z W X are right angles. Angle G F J is congruent to angle Y Z W, angle F G H is congruent to angle Z Y X, and angle G H J is congruent to angle Y X W.
What is the length of side WX
?
(1 point)
Scale Drawings Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration shows two similar quadrilaterals F G H J and Z Y X W. In the quadrilateral F G H J, side F J measures 5, side F G measures 6, and side H J measures 4. Side G H is unmeasured. In the quadrilateral Z Y X W, side Z W measures 10, side Z Y measures 12, and side Y X measures 14. Side XW is unmeasured. Angle F J H and angle Z W X are right angles. Angle G F J is congruent to angle Y Z W, angle F G H is congruent to angle Z Y X, and angle G H J is congruent to angle Y X W.
What is the length of side WX
?
(1 point)
Answers
GPT-4o mini
To find the length of side WX in quadrilateral ZYXW, we can use the fact that the two quadrilaterals FGHI and ZYXW are similar. This means that the ratios of corresponding sides are equal.
We know the corresponding sides of the similar quadrilaterals:
- FJ (5) corresponds to ZW (10)
- FG (6) corresponds to ZY (12)
- HJ (4) corresponds to YX (14)
To find the ratio, we can compare one of the pairs of corresponding sides:
For FJ and ZW:
\[
\frac{FJ}{ZW} = \frac{5}{10} = \frac{1}{2}
\]
For FG and ZY:
\[
\frac{FG}{ZY} = \frac{6}{12} = \frac{1}{2}
\]
For HJ and YX:
\[
\frac{HJ}{YX} = \frac{4}{14}
\]
We simplify \(\frac{4}{14}\):
\[
\frac{4}{14} = \frac{2}{7}
\]
Now we see the ratio isn't consistent for HJ and YX, suggesting that there might be an issue with the specifics of the question. However, these ratios indicate the similarity principle holds for FJ and ZW as well as FG and ZY.
Assuming the correct scaling and that the ratio applies consistently, we check the ratio we found:
\[
\text{If the side lengths perceived from ZY and their other respective sides are assumed scales of 1:2 or similar, let's apply that hence:}
\]
On intuition from the available data, let's find WX appropriately scaled relative to side correspondences.
Notably, if we apply one example from above, ZYXW's total is leading us to understand side WX, corresponds to side HJ given as 4, and confirmed becomes:
By assigning the direct measurement taking similar scaling:
Using \( \frac{4}{x} = \frac{1}{2} \) thus:
Assign \(x = WX\):
Final solving gives:
\[
\Rightarrow 4\cdot 2 = WX = 8 (consistent squared nature with ratios)
\]
So the length of side WX is \( \text{8 units} \).
We know the corresponding sides of the similar quadrilaterals:
- FJ (5) corresponds to ZW (10)
- FG (6) corresponds to ZY (12)
- HJ (4) corresponds to YX (14)
To find the ratio, we can compare one of the pairs of corresponding sides:
For FJ and ZW:
\[
\frac{FJ}{ZW} = \frac{5}{10} = \frac{1}{2}
\]
For FG and ZY:
\[
\frac{FG}{ZY} = \frac{6}{12} = \frac{1}{2}
\]
For HJ and YX:
\[
\frac{HJ}{YX} = \frac{4}{14}
\]
We simplify \(\frac{4}{14}\):
\[
\frac{4}{14} = \frac{2}{7}
\]
Now we see the ratio isn't consistent for HJ and YX, suggesting that there might be an issue with the specifics of the question. However, these ratios indicate the similarity principle holds for FJ and ZW as well as FG and ZY.
Assuming the correct scaling and that the ratio applies consistently, we check the ratio we found:
\[
\text{If the side lengths perceived from ZY and their other respective sides are assumed scales of 1:2 or similar, let's apply that hence:}
\]
On intuition from the available data, let's find WX appropriately scaled relative to side correspondences.
Notably, if we apply one example from above, ZYXW's total is leading us to understand side WX, corresponds to side HJ given as 4, and confirmed becomes:
By assigning the direct measurement taking similar scaling:
Using \( \frac{4}{x} = \frac{1}{2} \) thus:
Assign \(x = WX\):
Final solving gives:
\[
\Rightarrow 4\cdot 2 = WX = 8 (consistent squared nature with ratios)
\]
So the length of side WX is \( \text{8 units} \).