Question

Quadrilateral KMPT is dilated by a scale factor of 3/4 to create K'M'P'T'. The perimeter of quadrilateral KMPT is x units. What is the perimeter in units of quadrilateral K'M'P'T'?
A)X units B)3/4x units C)(3/4)squaredX units D)4/3X units

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Answer 1

Answer:

B) $\frac{3}{4}$ x units

Step-by-step explanation:

Let quadrilateral KMPT be a rectangle with dimensions 12 units by 8 units. Then its perimeter would be equal to:

Perimeter of a rectangle = 2 (l + b)

where: l is the length = 12 units and b is the breadth = 8 units. So that:

Perimeter of KMPT = 2 (12 + 8)

                               = 40 units

Dilating KMPT by a scale factor of $\frac{3}{4}$ would create K'M'P'T' of dimensions; $\frac{3}{4}$ × 12 units by $\frac{3}{4}$ × 8 units. Thus, the dimensions of K'M'P'T' would be 9 units by 6 units.

Perimeter of K'M'P'T' = 2 (l + b)

                                  = 2(9 + 6)

                                  = 30 units

Comparing the perimeters of KMPT and K'M'P'T', the perimeter of K'M'P'T' would be  $\frac{3}{4}$ × perimeter of KMPT.

Therefore, if the perimeter of KMPT is x units, then;

         perimeter of K'M'P'T' = $\frac{3}{4}$ * x units

                                            = $\frac{3}{4}$x units