Math Is Fun Forum

lakeheadca

Member

Registered: 2010-01-31

Posts: 37

Triangle ratio and midpoint

in the fig, triangle PQR ~ TUV. point S is the midpoint of QR AND POINT W is the midpoint of UV. If PR/TV = 3/5 WHAT IS THE VALUE OF THE FOLLOWING ratio?
Area of triangle PSR / Area of triangle TUV.
note:Large fig is not 90 degree, not to scale

Last edited by lakeheadca (2010-06-30 15:38:54)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Triangle ratio and midpoint

hi lakeheadca

I was just browsing for unanswered posts and found this.  So I thought about it, sorry it's been a long wait.

Not sure what you mean by 'triangle PQR ~ TUV'

See diagram below.  Any answer is possible if the midpoint and ratio constraints are the only ones.

But if 'triangle PQR ~ TUV' means the triangles are similar then it becomes possible.

The areas of PQR and TUV will be in the ratio (3/5) squared.

As area of any triangle is half base x height, the line up from the midpoint will bisect the area (same height but base is half as long for each half).

So, if PQR : TUV = 9 : 25 then PSR : TUV = 4.5 : 25 = 9 : 50

hth

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