this is the problem v

http://oi57.tinypic.com/2uj4n61.jpg

it's in image form so you can see the diagram

Relevance

Why so urgent? Isn't geometry about timeless things like triangles? ;-)

But let's try it: Call RW "x", as it's easier to write, and we want to find it; and WS is then x+2.

And TW = 5.

There are three similar right triangles, do look and see, please: SRT, TRW, and STW, and you need to mind which angles and sides are corresponding, so you can use the ratios (same as proportions).

Ratios of corresponding sides, in two of the triangles:

x/5 = 5/(x+2) and so, very simply it rearranges into:

x(x+2) = 5*5 = 25 so you end up with:

x^2 + 2x - 25 = 0, a quadratic equation in standard from. Then you use the Quadratic Formula that you've learnt by heart (or can easily look up), and discover that:

x = [ -1 ± √(4 + 100) ] / 2

= (-1/2) ± (√104)/2 Quick, use a calculator, nearest tenth...

= (-1/2) ± (10.20/2)

= 5.10 - 0.5

= 4.60

I do hope all that's right, you might rather check it all (I would but have to leave in a hurry, sorry...)

And I hope it helps. :-)

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• Anonymous
6 years ago

ok this is a proportion problem for the two smaller triangles within the bigger triangle. Because TW is an altitude it creates right angles, so you can know that these two triangles are proportional. you want to set up a ratio for the height of each triangle and the base of each triangle. so for triangle one height is to base (5/X). then the second triangle is also height to base but the height of the triangle is the x+2 so it is (x+2)/5. set these equal to each other then cross multiply. you should get 25=x(x+2). then distribute the x. so 25=x^2+2x. then subtract the 25 so it is 0=x^2(x squared)+2x+25. then factor. after you factor just solve for both x's and choose the positive one. that is x's value which is your answer!

Hope this helps!

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