I came across this question while I was taking one of the pratice Mu Alpha Theta tests for my school

Bruno Pittman

Bruno Pittman

Answered question

2022-07-12

I came across this question while I was taking one of the pratice Mu Alpha Theta tests for my school and I wasn't sure how to solve it. It reads: In Δ U S A, S is bisected by S Y , with Y on side U A ¯ . If all sides have integer values, U S ¯ = 18 and U Y ¯ = 12; find the smallest possible perimeter of Δ U S A.

The answer key with the solutions skipped to the part with the triangle inequalities, so that is why I am not sure what to do. I think there is some ratio when it comes to splitting a triangle with an angle bisector but I am not sure what it is. My question is how would I solve this question, and for future reference what is that ratio for an angle bisector in a triangle.

Answer & Explanation

Jaruckigh

Jaruckigh

Beginner2022-07-13Added 11 answers

Hint: The relevant theorem about angle bisectors (adapted to your labels) is
A Y Y U = S A S U .

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