Answer:
B) [tex]\frac{3}{4}[/tex] 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 [tex]\frac{3}{4}[/tex] would create K'M'P'T' of dimensions; [tex]\frac{3}{4}[/tex] × 12 units by [tex]\frac{3}{4}[/tex] × 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 [tex]\frac{3}{4}[/tex] × perimeter of KMPT.
Therefore, if the perimeter of KMPT is x units, then;
perimeter of K'M'P'T' = [tex]\frac{3}{4}[/tex] * x units
= [tex]\frac{3}{4}[/tex]x units
