rectangle ABCD is similar to rectangle wxyz , with AB corresponding to wx. if AB=24,BC=30 and wx=16 , what is the area of the rectangle wxyz
To find the area of rectangle WXYZ, we need to determine the relationship between the sides of the two rectangles. We are given that rectangle ABCD is similar to rectangle WXYZ, with AB corresponding to WX.
Since corresponding sides of similar rectangles are proportional, we can set up the following ratio:
AB/BC = WX/XY
Plugging in the given values, we have:
24/30 = 16/XY
To find the value of XY, we can cross-multiply and solve for XY:
24 * XY = 30 * 16
XY = (30 * 16) / 24
XY = 20
Now that we know the value of XY, we can calculate the area of rectangle WXYZ, which is given by:
Area(WXYZ) = WX * XY
Area(WXYZ) = 16 * 20
Area(WXYZ) = 320
Therefore, the area of rectangle WXYZ is 320 square units.
the ratio of the areas is NOT 1.5 : 1
it is 24^2 : 16^2 = 9 : 4
the area of the larger is 720 (see above)
so the area of the smaller is 4/9(720) = 320
You yourself found XY to be 20
so the area of the other rectangle is 16(20) = 320
Rectangle ABCD is similar to rectangle WYYZ.
Uf tge the area of rectangle ABCD is 90 square inches, what is the area of rectangle WXYZ?
the ratio of areas of similar figures is proportional to the square of their corresponding sides
area of ABCD = 24(30) = 720
WXYZ/720 = 24^2/16^2
solve for WXYZ