The scale of two similar quadrilaterals is 1:3. The perimeter of the smaller quadrilateral is 90 centimeters. What is the perimeter of the larger quadrilateral?
Perimeter = 3 * 90 = 270 cm
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To find the perimeter of the larger quadrilateral, we need to use the fact that the scale of the two quadrilaterals is 1:3.
The scale 1:3 means that every side of the smaller quadrilateral is 1 unit in length, while every corresponding side of the larger quadrilateral is 3 units in length.
Given that the perimeter of the smaller quadrilateral is 90 centimeters, we know that the sum of all four sides is 90 centimeters. Since each side of the smaller quadrilateral is 1 unit, the sum of all four sides is 4 units, which is equal to 90 centimeters.
To find the length of one unit, we can divide the sum of the four sides (90 centimeters) by the number of sides (4).
Length of one unit = Total sum of sides / Number of sides
= 90 centimeters / 4
= 22.5 centimeters
Now that we know the length of one unit is 22.5 centimeters, we can multiply this length by 3 to find the length of each side of the larger quadrilateral.
Length of each side of the larger quadrilateral = Length of one unit x Scale ratio
= 22.5 centimeters x 3
= 67.5 centimeters
Since the larger quadrilateral has four sides, its perimeter is given by the sum of all four sides.
Perimeter of the larger quadrilateral = Length of each side x Number of sides
= 67.5 centimeters x 4
= 270 centimeters
Therefore, the perimeter of the larger quadrilateral is 270 centimeters.