Question

I need help on 21-26....explaining how to do it would be nice and if you could work one out and explain it that would be nice too...thank you

Answer 1

Triangles ABC and DEF are similar, which means corresponding sides occur in ratios with one another. Mathematically, this means

$\dfrac ad=\dfrac be=\dfrac cf$

Also, corresponding angles are congruent. These are A and D, B and E, C and F.

As an example, for 21, the above equation turns into

$\dfrac a5=\dfrac b4=\dfrac{11}6$

and you can solve for $a$ and $b$ directly:

$\dfrac a5=\dfrac{11}6\implies6a=55\implies a=\dfrac{55}6$

$\dfrac b4=\dfrac{11}6\implies6b=44\implies a=\dfrac{44}6=\dfrac{22}3$

The others are solved exactly the same way. In each case, you happen to be given all the side lengths for one of the triangles, and one of the side lengths for the other triangle. So all you need to do is plug in what you know and solve for the remaining two sides.