PLEASE HELP ASAP

The solution of the first image is: b = √48

The solution of the second image is: c = √125

Step-by-step explanation:

Here we have two triangle rectangles, first, we need to remember the Pythagorean theorem.

For a triangle rectangle with cathetus A and B, and a hypotenuse H, we have the relationship:

A^2 + B^2 = H^2

Where H is the side that is opposite to the right angle (the angle of 90°)

In the first image, we can see that the hypotenuse is equal to 8, and one cathetus is equal to 4.

We want to find the value of b, that is the other cathetus.

Then we have:

4^2 + b^2 = 8^2

b^2 = 8^2 - 4^2

b^2 = 48

b = √48

Second image:

in this case, c is the hypotenuse, a and b are the cathetus.

We know that:

a = 5, b = 10

Then we have the equation:

a^2 + b^2 = c^2

Now we can replace the above values:

5^2 + 10^2 = c^2

25 + 100 = c^2

125 = c^2

√125 = c

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.