Let's walk through the steps together!
Step-by-step explanation:
1
a) we know that the Pythagorean theorem is a^2+b^2=c^2
a^2+b^2=c^2 means that if we add the squared values for each of the two sides of the triangle (these sides need to have an angle of 90 degrees together. Basically they are the ones that aren't the hypotenuse) we get the value of the hypotenuse (the longest side that doesn't help to make the right angle).
We see that we have the values of a and b in this formula (these sides need to have an angle of 90 degrees together.) Plugging the values in problem 1a into this formula, we see that 16^2+12^2=x^2 (x is the value we need to find)
16^2=236
12^2=144
so the formula now says that 236+144=x^2
236+144=400, so x= 
, which is 20.
so x=20
b) we can use the same knowledge we used in the first problem in this problem as well. In this problem, we are given the values of c (the hypotenuse) and one of the sides (which for our purposes can be a).
a^2+b^2=c^2 -> 100+b^2=289
This means that b=
so b=
so b=
2
These ones are pretty basic, having any common knowledge of ratios should lead you right to the answer. I will help you with a and d
a) we are given the values 6 and 9 as a ratio, which is the same as a 2:3 ratio. 12 corresponds to 6, so 12 would be the 2 in 2:3, meaning the answer (for the value of x) is 18
d) we are given the values 6 and 8, and the corresponding value to 8 is 12. 6 and 8 make a ratio of 3:4, and if we plug 12 in as the 3, the 4->4*4=16
3
I can't see the full problem so unfortunately, I cannot help you
I hope this helped in your understanding!
-Suvi
