Hints:

in these 2 tough geometry/similarity questions from past final exams, it really helps to

1 -- use colors to outline the triangles you're comparing

2 -- identify the angles with letters

3 -- look for all proportions that might lead to the solution.

Go to it.

1)

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2) Measures are as shown in cm. Find the length of EF.

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Solutions

1)

Step 1: find h using Pythagoras: h = 29.14

Step 2: compare big red ABC to small blue ABH

c marks the common angle in the triangles, o marks the others

base = 12.57 + 63 = 75.57, h = 29.14

Area = ½ bh = 1063.36 cm²

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2) Measures are as shown in cm. Find the length of EF.

Label EF as x and CF as a.
Now we compare triangles AEF and ABC (big/small)

Now we compare triangles AFG and ACD (big/small)

So,

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