Question

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Answer 1

You can do this if you realize the triangles are similar, which means they have the same angles. Each of the small triangles is similar to the big one, because:

1. big one has 90 degree angle, small one also.
2. big one and small one have one angle in common, so they are equal

Now big and small triangle have two angles in common, so they are similar.
Now that we know they are similar, the small ones are also similar to each other.

All this means: the ratio of sides is constant:

y/12=(12+16)/y (ratio of two sides of left triangle and big triangle) so:

y/12=28/y

In the same way: x/16=(12+16)/x, (right triangle and big one) so:

x/16=28/x

Can you solve these equations?

Answer 2

Just calculate the square root of 336

Answer 3

You'll get\[y=\sqrt{336}=\sqrt{16 \cdot 21}=4\sqrt{21}\]or about 18.3

Answer 4

Right!

Answer 5

YW!