Math Is Fun Forum

CoRRupt3d

Guest

Problem:

Need help with this difficult Geometry Problem:

Sue and Barry are trying to find the area of triangle ABC. Sue mistakenly uses AB and the height from A (instead of the height from  C), and Barry mistakenly uses BC and the height from C (instead of the height from A)

(a)Sue finds an area of 12 and Barry finds an area of 27. What is the area of triangle ABC?

(b) Suppose instead that Sue finds an area of 120 and Barry finds an area of 150. Now what is the area of triangle ABC?

I drew a diagram, but I don't know how to find the area of triangle ABC!

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Problem:

Imagine triangle ABC. Draw an altitude from A to BC, and another one from C to BA. We'll call the place where A meets BC D and C meets AB E.

For (a)

Sue:

Barry:

Isolating the bases and the altitudes gives

and

Multiply those 2 equations together and do a couple of operations to get

and then divide by 2!

(b) Just repeat the process used on (a)