There is on large rectangle ABCD, top line is AD and bottom is BC.
A line is drawn from the top to bottom called GH.
A line is drawn from left to right called EF.
AEFG is Rectangle 1.
EBHF is Rectangle 2.
GHCD is Rectangle 3.
All three rectangles are similar.
Length of line AE is 4cm.
Length of line EB is 9cm.
What is the area of rectangle GHCD ? another rectangle within ABCD called
To find the area of rectangle GHCD, we need to find the length and width of the rectangle.
Since all three rectangles (AEFG, EBHF, and GHCD) are similar, their corresponding sides are proportional.
From the given information, we have:
Length of AE = 4 cm
Length of EB = 9 cm
By comparing the corresponding sides of rectangles AEFG and EBHF, we can determine the ratio of their lengths:
Length of AE / Length of EB = Length of AEFG / Length of EBHF
Plugging in the values, we get:
4 cm / 9 cm = Length of AEFG / Length of EBHF
Cross-multiplying, we have:
9 * Length of AEFG = 4 * Length of EBHF
Simplifying, we find:
Length of AEFG = (4/9) * Length of EBHF
Since Rectangle 3 (GHCD) is also similar to rectangles AEFG and EBHF, we can use the same ratio to find its length:
Length of GHCD = (4/9) * Length of EBHF
Now, we need to find the width of GHCD. To do this, we compare the corresponding sides of rectangles AEFG and GHCD:
Length of AE / Length of GH = Length of AEFG / Length of GHCD
Plugging in the given values, we have:
4 cm / ? = (4/9) * Length of EBHF / Length of GHCD
Cross-multiplying, we get:
4 * Length of GHCD = (4/9) * Length of EBHF * Length of GH
Simplifying, we find:
Length of GHCD = (4/9) * Length of EBHF * Length of GH / 4
Using the values given, we can plug them into the formula to find the length and width of GHCD:
Length of GHCD = (4/9) * 9 cm * ? cm / 4
Note that we still need to know the length of GH to calculate the area of GHCD. If you have that information, please provide it, and then we can easily find the area of rectangle GHCD.