Triangle - finding base length of smaller triangle within bigger triangle - no angles given and only one side!

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Triangle A-P-Q is the bigger triangle with an area of 99 cm^2. Triangle A-B-C has an area of 11 cm^2. B-C is parallel to PQ and the length of P-Q is 12 cm. I need to calculate the length of B-C.

We know that the triangles are similar and we know that in general you would use the scale factor to determine this answer. However, we only know the length of one side so we cannot determine the scale factor. We do know the areas of each triangle but we are stuck on how to use this information to help us find the length of B-C. Is anyone familiar with the method to solve this question? Thank you!

Posted Sun 24th February, 2013 @ 13:40 by Isabella

1 Answer

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Got it figured out, I think. The similarity ratio is the square root of the area ratio which is 1:9 so similarity ratio is 1:3, and so the base of B-C is 4 cm and the height is 5.5 cm which works out to the correct area of 11 cm ^2. Therefore, the answer is 4 cm.

Answered Sun 24th February, 2013 @ 14:01 by Isabella
Edited by Isabella on Sun 24th February, 2013 @ 14:04