Respuesta :
Answer:
Rectangle ABCD is similar to Rectangle WXYZ .
When two polygons( Rectangle) are similar their interior angles are equal i.e equal to 90° and sides are proportional.
[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}[/tex]
Let this ratio be equal to m.
If m>1, then Rectangle A B CD has expanded.
If 0<m<1, then Rectangle A B CD has Shrank.
So,⇒ W X= m× AB→[Larger Rectangle] Or ⇒ m× W X= AB→[Smaller rectangle}
⇒X Y= m× B C→[Larger Rectangle] Or⇒ m ×X Y= B C→[Smaller rectangle}
⇒As ,Area of A B CD = 30 square inches
⇒Length × Breadth = 30 square inches
⇒ AB×CD = 30 square inches
⇒W X/m × X Y/m= 30 square inches
⇒Area(Enlarged Rectangle W X Y Z)=30×m² square inches
If the Rectangle has shrank by m units , then
Area(Rectangle W X Y Z)=[tex]\frac{30}{m^2}[/tex] square inches
Answer:
Area of rectangle WXYZ = ( Area of rectangle ABCD ) / [tex]k^2[/tex]
Step-by-step explanation:
We know that two polygons are said to be similar if their sides are proportional.
As ABCD and WXYZ are similar,
[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}[/tex]
Let this ratio be equal to k,
So,
[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}=k\\AB=k\,WX\,,\,BC=k\,XY\,,\,CD=k\,YZ\,,\,AD=k\,WZ[/tex]
Area of rectangle ABCD = 30 square inches = length × breadth = AB × BC = k WX × k XY = [tex]k^2[/tex] WX × XY = [tex]k^2[/tex] × Area of rectangle WXYZ.
So, if know value of k, we can find area of rectangle WXYZ
i.e, Area of rectangle WXYZ = ( Area of rectangle ABCD ) / [tex]k^2[/tex]
