There is one large rectangle ABCD, top line is AD and bottom is BC.
A vertical line is drawn from the top to bottom called GH (between points AD and BC).
A line is drawn from left to right called EF (between points AB and GH).
AEFG is Rectangle 1.
EBHF is Rectangle 2.
GHCD is Rectangle 3.
All three rectangles are similar.
Length of line AE (vertical) is 4cm.
Length of line EB (vertical) is 9cm.
What is the area of rectangle GHCD ?
I did not answer this question before, because I found it confusing.
AEFG EBHF are not rectangles
Is there a point named for the intersection of GH and EF ?
Check your typing.
I don't see a problem but I will rewrite the structure.
Make two rectangles attached together.
Call the first rectangle ABHG (AG top, BH bottom).
Call the second rectangle GHCD (HC top, GD bottom).
Draw a horizontal line from line AB to line GH and name the points E on line AB and F on line GH.
example:
A----G-------------D
|....|.............|
|....|.............|
E----F.............|
|....|.............|
|....|.............|
|....|.............|
|....|.............|
B----H-------------C
Rectangles AEFG, EBHF and GHCD are similar.
The length of AE is 4cm.
The length of EB is 9cm.
What is the area of rectangle GHCD ?
Look at your diagram and trace out
figure AEFG, it does not form a rectangle.
the same is true for EBHF.
Also, it is proper notation to list the order of letters of similar shapes so that line segments correspond.
e.g.
If I were to say triangle ABC is similar to triangle PQR
then, without looking at the diagram, I can tell that
AB/AC = PQ/PR etc.
I think we have to call the intersection of EF and GH something like K
So did you mean rectangle AEKG is similar to rectangle EBHK ?
How do the sides line up?
I think it would have to be something like
AE/EK = EK/EB
I reposted a better structure at 1:58
thank you for your help so far.
To find the area of rectangle GHCD, we need to determine its dimensions. Since all three rectangles are similar, we can use the given information of the lengths of the vertical sides of rectangle AEFG (4cm) and EBHF (9cm) to find the corresponding lengths of GHCD.
Since AEFG and GHCD are similar rectangles, their corresponding sides are proportional. This means that the ratio of the lengths of their corresponding sides is the same.
Let's denote the length of GHCD as xcm. Since AE = 4cm and GH corresponds to EB, we can set up the following proportion:
AE / GH = EB / x
Plugging in the given values, we have:
4 / GH = 9 / x
To find x, we can cross-multiply and solve for x:
4x = 9 * GH
Now, let's look at the information provided in the problem. The length of AE (vertical) is given as 4cm, and the length of EB (vertical) is given as 9cm. The length of EB is composed of GH + HB, so we have:
EB = GH + HB
9 = GH + HB
Now let's substitute GH + HB for EB in the equation above:
4x = 9 * (GH + HB)
Now, we know that the length of GH + HB is 9 (from the given information). Let's substitute that into the equation:
4x = 9 * 9
4x = 81
Now, divide both sides by 4 to solve for x:
x = 81 / 4
x = 20.25
So, the length of GHCD is 20.25 cm.
To find the area of GHCD, we multiply the length (20.25 cm) by the width (which is the same as AE or EB, so it's 4 cm). Therefore, the area of GHCD is:
Area = length * width
Area = 20.25 cm * 4 cm
Area = 81 cm²
The area of rectangle GHCD is 81 square centimeters.