Math CentralQuandaries & Queries


Question from Meagan, a student:

Here is my problem: Three congruent (non-square) rectangles are placed
to form a larger rectangle. [Two are oriented the same way and the
"stacked" while the third is rotated 90 degrees and placed next to the
other two.] The total area is 1350 square centimeters. Square ABCD is
then created that has the same perimeter as the large rectangle that was
created. E is the midpoint of line CD and F is the midpoint of BC. Find the
area of triangle AEF.

Hi Meagan,

I called the lengths of the triangles L centimeters, the widths W centimeters and put them together the way you described.


From the diagram the area is (L + W) × (2W) which is 1350 square centimeters. Look at the diagram, what relationship can you see between L and W? Substitute this into the area relationship above and solve for L and W.

Can you see now how to complete the solution?


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