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**lakeheadca****Member**- Registered: 2010-01-31
- Posts: 37

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)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,651

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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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