## Thursday, March 2, 2023

### Geometry Problem 1517: Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School.

Geometry Problem 1517. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

More Details

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

#### 5 comments:

1. V6 (sqrt of 6)

1. https://photos.app.goo.gl/CkcFLDMpaKUyBK3a9

2. Drop perpendiculars DP and DQ from D to AB and from D to BC, P on AB and Q on BC respectively.

Since AD = DC, S(ABD) = S(BDC)

So AB.DP/2 = BC.DQ/2

Hence (c/2)d/(sqrt2) = (1/2).2. (sqrt3./2)d
Simplifying c = sqrt 6

Sumith Peiris
Moratuwa
Sri Lanka

3. Construct parallelogram BAEC.
Drop perpendicular AH, from A to BE.
AEH is a 30-60-90 triangle, and ABH is a 45-45-90 triangle.
BC=AE=2, AH=sqrt 3, AB=sqrt 6.

4. AB/AD = sin D / sin 45.
DC/BC = sin 60 / sin 45.
Multiply side by side
AB/BC = sqrt 3 / sqrt 2 => AB = sqrt 6.