# Can You Solve This MIT Admissions Question? Geometry Problem, 1869

The Massachusetts Institute of Technology (MIT) is one of the top ranked universities in the world. This question appeared on its admissions exam nearly 150 years ago. “The perpendicular dropped from the vertex of the right angle upon the hypotenuse divides it into two segments of 9 and 16 feet respectively. Find the lengths of the perpendicular, and the two legs of the triangle.” The video presents a solution.

Blog post: http://wp.me/p6aMk-4KU

Sources

MIT Questions: https://libraries.mit.edu/archives/exhibits/exam/geometry.html

MIT Answers: https://libraries.mit.edu/archives/exhibits/exam/geometry-answers.html

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: http://mindyourdecisions.com/blog/

Twitter: http://twitter.com/preshtalwalkar

Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965

Google+: https://plus.google.com/108336608566588374147/posts

Pinterest: https://www.pinterest.com/preshtalwalkar/

Tumblr: http://preshtalwalkar.tumblr.com/

Instagram: https://instagram.com/preshtalwalkar/

Patreon: http://www.patreon.com/mindyourdecisions

Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r

My Books

“The Joy of Game Theory” shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444

“The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias” is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/

“Math Puzzles Volume 1” features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/

“Math Puzzles Volume 2” is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/

“Math Puzzles Volume 3” is the third in the series. https://www.amazon.com/gp/product/1517596351/

“40 Paradoxes in Logic, Probability, and Game Theory” contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/

“The Best Mental Math Tricks” teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/

“Multiply Numbers By Drawing Lines” This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/

**Video Rating: / 5**

It's just the geometric mean. That's ez light shit.

So, there's enough people on earth you can't solve this? really???

θεμα εξετασεων β λυκ

more like an SAT leveled question…

shit man,, it took me about 50 secs. fuck

this is so easy OMG I would take an A with this

I reached the point where p/16 = 9/p with Trigonometry but then I didn't know what to do after. Great Video!

I took Geometry this year, so it wasn't that hard

Not hard…. I'm guessing this was one of the easier questions. Any smart 12-14 year old should get the answer.

This is super easy ! I mean how can this be an admission test ?

Prove that these triangles are similar…

Very easy only requires a cool mind

no need of any ratios, In India, we encounter these sort of Questions in !0th or 9th grade probably.

finally one i could solve -__-

It can be solved too if you just know that in a rectangle triangle the vertex of the right angle lies in a circle whose center is in the middle point of the oter two vertex. In that case:

r=(9+16)/2=12.5

The ecuation of a circle with r=12.5 is

x^2+y^2=12.5^2

In the Point of Interest x= 16-12.5 = 3.5

We can obtain y (p in the point of interest) by

y = sqrt(12.5^2-3.5^2) = 12

I cant guess why physicists like me are supposed to be weird people… ¯_(ツ)_/¯

It can be solved easily with pitagoras

based on the catheus theorem the altitude of a right triangle towards the hypotenuse equals the square root of the the product of the 2 lengths of the hypotenuse split by the altitude

Easy peasy lemon squeezy

Since the big triangle is a right triangle we could use the formula p = 1/2*25= 12.5

Once we find p, the rest is easy