Quadrilateral KMPT is dilated by a scale factor of 34 to create quadrilateral K′M′P′T′. The perimeter of quadrilateral KMPT is x units. What is the perimeter in units of quadrilateral K′M′P′T′?
Answers
Given : Quadrilateral KMPT is dilated by a scale factor of 34 to create quadrilateral K′M′P′T′.
The perimeter of quadrilateral KMPT is x units
To Find : perimeter in units of quadrilateral K′M′P′T
Solution:
Shapes reflected / dilated , translated remains similar
Quadrilateral KMPT is dilated by a scale factor of 34 to create quadrilateral K′M′P′T′.
Hence
quadrilateral K′M′P′T′ ≈ Quadrilateral KMPT
Ratio of perimeter of similar quadrilateral = ratio of corresponding sides
dilated by a scale factor of 34
Hence ratio of corresponding sides = 34
Perimeter of quadrilateral K′M′P′T′ = 34 Perimeter of quadrilateral KMPT
=> Perimeter of quadrilateral K′M′P′T′ = 34x units
Perimeter of quadrilateral K′M′P′T′ = 34x units
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Solution:
Shapes reflected / dilated , translated remains similar
Quadrilateral KMPT is dilated by a scale factor of 34 to create quadrilateral K′M′P′T′.
Hence
quadrilateral K′M′P′T′ ≈ Quadrilateral KMPT
Ratio of perimeter of similar quadrilateral = ratio of corresponding sides
dilated by a scale factor of 34
Hence ratio of corresponding sides = 34
Perimeter of quadrilateral K′M′P′T′ = 34 Perimeter of quadrilateral KMPT
=> Perimeter of quadrilateral K′M′P′T′ = 34x units
Perimeter of quadrilateral K′M′P′T′ = 34x units