Question
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Two quadrilaterals are shown. One is slightly smaller than the other. Both shapes have a right angle marker in their top left and bottom left corners. Both shapes have a curved angle marker in their top right corners. Both shapes have two curved angle markers in their bottom right corners. The larger shape has its top side marked x minus 1, its right side marked y plus 1, its bottom side marked 32, and its left side marked 16. The smaller shape has its top side marked 6, its right side marked 21, its bottom side marked 24, and its left side marked 12.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
To find the value of x, we can set up a proportion using the corresponding sides of the two quadrilaterals.
We have the following sides:
For the larger quadrilateral:
Top side = x - 1
Right side = y + 1
Bottom side = 32
Left side = 16
For the smaller quadrilateral:
Top side = 6
Right side = 21
Bottom side = 24
Left side = 12
Set up the proportion:
(x - 1)/6 = 16/12
Cross multiply to solve for x:
12(x - 1) = 6 * 16
12x - 12 = 96
Add 12 to both sides:
12x = 108
Divide both sides by 12:
x = 9
Therefore, the value of x is 9.