'08 q10 (1 Viewer)

[Makro]

Part b)

The diagram shows two parallel brick walls KJ and MN joined by a fence from J to M. The wall JK is s metres long and <kjm the="" fence="" jm="" is="" l="" metres="" long.="">

A new fence is to be built from K to a point P somewhere on MN. The new fence KP will cross the original fence JM at O.

Let OJ = x metres, where 0 < x < L.

i) Show that the toal area, A square mentres, enclosed by triangle OJK and triange OMP is given by

A = s( x - L + (L²/2x))sin(alpha)

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Area of triangle is 1/2absinC from what I know. Why does it prove that the two triangles are similar in the book? I don't understand why they're proven to be similar. Where does it ask for or need that?
</kjm>

 

[kelllly]

You need to prove that the triangles are similiar to find the length of MP.

Area of triangleOMP
= 1/2 x OM x MP x sin(angleOMP)